MA140 Calc for Busin and Soc Science Chapter 3: Complete Edition

Provide an appropriate response. A point is moving on the graph of xy = 24. When the point is at (4, 6), its x coordinate is increasing at the rate of 9 units per second. How fast is the y coordinate changing at that moment?

decreasing at 27/2 units per second

Solve the problem. The demand equation for a certain product is 5p^2 + q^2 = 1,300, where p is the price per unit in dollars and q is the number of units demanded. Find dq/dp.

dq/dp = -5p/q

Solve the problem. The position of a particle at time t is given by s, where s^3 + 8st + 4t^3 - 12t = 0. Find the velocity ds/dt.

ds/dt = 12-8s-12t^2/3s^2+8^2.

Provide an appropriate response. Find dy/dx by implicit differentiation. x^3 + y^3 = 5

dy/dx = - x^2/y^2

Differentiate. Find dy/dx for y = x^3/x-1.

dy/dx = 2x^3-3x^2/(x-1)^2

Find the derivative. y = (x^-2 + x)^-3

dy/dx = 3x^5(2-x^3)/(1+x^3)^4

Provide an appropriate response. Find dy/dx by implicit differentiation. x^3 + 3x ^2y + y^3 = 8

dy/dx = x^2+2xy/x^2+x^y

Provide an appropriate response. Find dy/dx by implicit differentiation. 2xy - y^2 = 1

dy/dx = y/y-x

Differentiate. Find f '(x) for f(x) = (5x^3 + 4)(3x^7 - 5).

f'(x) = 150x^9 + 84x^6 - 75x^2

Differentiate. Find f '(x) for f(x) = (2x - 4)(2x^3 - x^2 + 1).

f'(x) = 16x^3 - 30x^2 + 8x + 2

Differentiate. Find f '(t) for f(x) = (3x - 4)(4x^3 - x^2 + 1)

f'(x) = 48x^3 - 57x^2 + 8x + 3

Find the derivative. Find f '(x) for f(x) = (4x^2 + 3x)^2.

f'(x) = 64x^3 + 72x^2 + 18x

Provide an appropriate response. Find f '(x) for f(x) = (4x^2 + 3x)^2.

f'(x) = 64x^3 + 72x^2 + 18x

Differentiate. Find f '(t) if f(t) = 0.4t(5t^2 + 1) and simplify.

f(t) = 6t^2 + 0.4

Provide an appropriate response. Consider the function: f(x) = 1/√11-x^2. Choose the answer choice that includes all of the pair(s) of functions from the list so that f(x) can be written as a composition: f(x) = g(h(x)).

g(x) = 1/√11-x; h(x) = x^2

Provide an appropriate response. Find the values of x where the tangent line is horizontal for the graph of f(x)=4x^2/x+2.

x = 0, x = -4

Provide an appropriate response. Find y' for y = y(x) defined implicitly by 3xy - x^2 - 4 = 0.

y = 2x - 3y/3x

Find all values of x for the given function where the tangent line is horizontal. f(x) = x/(x^2+1)^3

±√5/5

Solve the problem. What will the value of an account (to the nearest cent) be after 8 years if $100 is invested at 6.0% interest compounded continuously?

$161.61

If $5,000 is invested at 5.25% compounded continuously, what is the amount in the account after 10 years?

$8,452.29

Provide an appropriate response. Find dy/dx for y = -5x^3-5x^2+3/-5x^4+2. Do not simplify.

(-5x^4+2)(-15x^2-10x)-(-5x^3-5x^2+3)(-20x^3)/(-5x^4+2)^2

Provide an appropriate response. Find the composition f[g(x)] if f(u) = u^5 and g(x) = 2 - 3x^2.

(2 - 3x^2)^5

Provide an appropriate response. Assume x = x(t) and y = y(t). Find dx/dt if x^2 (y - 6) = 12y + 3 and dy/dt = 2 when x = 5 and y = 12.

- 13/30

Find the derivative. Find f '(x) for f(x) = (8x - 9)^-4.

- 32/(8x-9)^5

Use appropriate properties of logarithms to rewrite f(x), and then find f'(x). f(x) = 1 + ln 5/x^4

- 4/x

Differentiate. Find f '(t) for f(x) = x/4x-6

- 6/(4x-6)^2

Find f'(x). f(x) = -2e^x + 9x - 4

-2e^x + 9

Differentiate. Find y' for y = x^2/9-2x

-2x^2-18x/(9-2x)^2

Provide an appropriate response. Assume x = x(t) and y = y(t). Find dx/dt if x^2 + y^2 = 25 and dy/dt = 3 when x = 3 and y = 4.

-4

Find dy/dx for the indicated function y. y = -4 ln x + 7 log 5 x

-4/x + 7/xln5

Find the derivative. Find d/dw 4/(w^2+3)^5

-40w/(w^2+3)^6

Find the percentage rate of change of f(x) at the indicated value of x. Round to the nearest tenth of a percent. f(x) = 4500 - 4x^2; x = 20

-5.5%

Find f'(x). f(x) = -7 ln x - x^5 + 2

-7/x - 5x^4

Provide an appropriate response. Find: lim 5000e -0.07t x ⇨ ∞

0

Solve the problem. Suppose that $8000 is invested at an interest rate of 5.5% per year, compounded continuously. How long would it take to double the investment?

12.6 yr

Solve the problem. How long will it take money to double if it is invested at 5.25% compounded continuously? Round your answer to the nearest tenth.

13.2 yr

Find the percentage rate of change of f(x) at the indicated value of x. Round to the nearest tenth of a percent. f(x) = 200 + 50x; x = 3

14.3%

Differentiate. Find f '(t) for f(x) = 2x-7/3x-2

17/(3x-2)^2

Provide an appropriate response. Find dy/dt for y = (5t^2 - 4t)^2.

2(5t^2 - 4t)(10t-4)

Provide an appropriate response. Find t to four decimal places. e^-t = 0.06

2.8134

Provide an appropriate response. Evaluate dy/dt for the function at the point. x^3 + y^3 = 9; dx/dt = -3, x = 1, y = 2

3/4

Find f'(x). f(x) = ln x^3 - 8e^x + 2x^2

3/x - 8e^x + 4x

Provide an appropriate response. A man 6 ft tall walks at a rate of 5 ft/sec away from a lamppost that is 13 ft high. At what rate is the length of his shadow changing when he is 65 ft away from the lamppost?

30/7 ft/sec

Find f'(x). f(x) = 3e^x - 8x + 2

3e^x - 8

Provide an appropriate response. A 26-foot ladder is placed against a wall. If the top of the ladder is sliding down the wall at 2 feet per second, at what rate is the bottom of the ladder moving away from the wall when the bottom of the ladder is 10 feet away from the wall?

4.8 ft/sec

Provide an appropriate response. Find t to four decimal places. e^-0.07t = 0.05

42.7962

Find dy/dx for the indicated function y. y = 5 + 2x^2 - 7^x

4x - 7^x ln 7

Use appropriate properties of logarithms to rewrite f(x), and then find f'(x). f(x) = 5x + 4 ln 2x

5 + 4/x

Solve the problem. How long will it take for $8400 to grow to $14.600 at an interest rate of 9.4% if the interest is compounded continuously? Round the number of years to the nearest hundredth.

5.88 yr

Find f'(x). f(x) = ln x^5

5/x

Provide an appropriate response. Find the composite g[f(-k)] if f(x) = 8x^2 - 5x and g(x) = 7x + 9.

56k^2 + 35k + 9

Provide an appropriate response. Find f'x for f(x) = (3x+4)^2/x^3-x^2+3x. Do not simplify.

6(x^3-x^2+3x)(3x+4)-(3x+4)^2(3x^2-2x+3)/(x^3-x^2+3x)^2

Find f'(x). f(x) = ln x^6 - 3x^2

6/x - 6x

Find dy/dx for the indicated function y. y = 3x^2 - log 3 x

6x - 1/xln3

Find dy/dx for the indicated function y. y = 7 log x

7/xln10

Provide an appropriate response. Suppose two automobiles leave from the same point at the same time. If one travels north at 60 miles per hour and the other travels east at 45 miles per hour, how fast will the distance between them be changing after three hours?

75 mph

Provide an appropriate response. Find x to two decimal places. x = 7,000e^0.11

7813.95

Find the derivative. Find: d/dx [8√8x^7-10]

7x^6/(8x^7-10)^7/8

Provide an appropriate response. A 26-foot ladder is placed against a wall. If the top of the ladder is sliding down the wall at 3 feet per second, at what rate is the bottom of the ladder moving away from the wall when the bottom of the ladder is 9 feet away from the wall?

8.1 ft/sec

Solve the problem. How long will it take for the value of an account to be $890 if $350 is deposited at 11% interest compounded continuously? Round your answer to the nearest hundredth.

8.48 yr

Find dy/dx for the indicated function y. y = 8^x

8^x ln 8

Find dy/dx for the indicated function y. y = 8^x - e^3

8^x ln 8

Find f'(x). f(x) = 8e^x + 4 ln x^3

8e^x + 12/x

Find f'(x). f(x) = x^8 + 3e^x

8x^7 + 3e^x

Solve the problem. An investor buys 100 shares of a stock for $20,000. After 5 years the stock is sold for $32,000. If interest is compounded continuously, what annual nominal rate of interest did the original $20,000 investment earn? (Represent the answer as a percent to three decimal places.)

9.400%

Find f'(x). f(x) = 3 ln x + ln x^6 + 4e^x

9/x + 4e^x

Find f'(x). f(x) = 9e^x - 2x^4

9e^x - 8x^3

Provide an appropriate response. Find dy/dx for y = ln (3x^3 - x^2)

9x-2/3x^2-x

Provide an appropriate response. Consider the function: f(x) = √9-x^2/x^2. Choose the answer choice that includes all of the pair(s) of functions from the list so that f(x) can be written as a composition: f(x) = g(h(x)).

Both A and B

Find the elasticity of the demand function as a function of p. x = D(p) = 500/(p+8)^2

E(p) = 2p/p+8

Find the elasticity of the demand function as a function of p. x = D(p) = √700-p

E(p) = p/1,400-2p

Find the elasticity of the demand function as a function of p. x = D(p) = 800 - p

E(p) = p/800-p

Use the price-demand equation to determine whether demand is elastic, is inelastic, or has unit elasticity at the indicated values of p. x = f(p) = 214 - 5p; p = 31.

Elastic

Use the price-demand equation to find the values of p which meet the given condition of elasticity. x = f(p) = 216-2p^2; determine the values of p for which demand is elastic and the values of p for which demand is inelastic..

Elastic on (6, 6 √3), inelastic on (0, 6)

Solve the problem. A beverage company works out a demand function for its sale of soda and finds it to be x = D(p) = 2,900 - 21p where x = the quantity of sodas sold when the price per can, in cents, is p. At what prices, p, is the elasticity of demand inelastic?

For p < 69 cents

Provide an appropriate response. Write composite function y = (2x^4 + 3x + 1)^3 in the form y = f(u) and u = g(x).

IDK yet

Use the price-demand equation to determine whether demand is elastic, is inelastic, or has unit elasticity at the indicated values of p. x = f(p) = 2005 - p^2; p = 13

Inelastic

Use the demand equation to find the revenue function. x = f(p) = 30(15 - p)

R(p) = 450p - 30p^2

Use the price-demand equation to find the values of p which meet the given condition of elasticity. x = f(p)= 168 - 7p; determine the values of p for which demand has unit elasticity. Round to two decimal places if necessary.

Unit at p = 12

Use the price-demand equation to determine whether demand is elastic, is inelastic, or has unit elasticity at the indicated values of p. x = f(p) = 1500 - 5p^2; p = 10

Unit elastic