9/15 Homework

8. Compute f '(x) using the limit definition. f(x) = x2 + 16x f '(x)= _________

2x+16

3. Use the limit definition to calculate the derivative of the linear function. f(x) = 9x − 8 f '(x)= ______

f'(x) = 9

2. For which values of x is f '(x)< 0? WebAssign Plot a) 7 < x < 9 b) 0 < x < 3 and x = 7 c) 3 < x < 7 d) 5 ≤ x ≤ 7 e) 3 < x < 5

a is the answer (7 < x < 9)

5. a) Use the limit definition to compute the derivative of the function at x = 2. f(x) = 7x−1 f '(2) = __________ b) Find an equation of the tangent line at x = 2. (Enter your answer as an equation using the variables y and x.) __________________

a) -7/4 b) unknown

4. a) Use the limit definition to compute f '(a). f(x) = 10 − x2, a = −1 f '(a) =_________ b) Find an equation of the tangent line. (Enter your answer as an equation using the variables y and x.) _________________

a) f'(a) = 2 b) y=2x+11

7. Each of the following limits represents a derivative f '(a). Find f(x) and a. a) lim (4 + h)^3 − 64/h h→0 f(x) =__________ a = 4 b) lim x→2 x^3 − 8/x − 2 f(x) = __________ a = 2 c) lim h→0 4^2 + h − 16/h f(x) = __________ a = 2

a) x^3 b) x^3 c)4^x

6. a) Use the limit definition to compute f '(a). f(x) = sqrt of (x + 2), a = 1 f '(a) = ____________ b) Find an equation of the tangent line. (Enter your answer as an equation using the variables y and x.) __________________

a)1/2(sqrt of 3) b)unknown

Let f(x) be the function whose graph is shown below. WebAssign Plot Determine the following. f '(1)= f '(3)= f '(5)= f '(8)= Estimate f '(7). (Round your answer to one decimal place.) Compare f '(6.5) and f '(7.5): f '(6.5) > f '(7.5) OR f '(6.5) < f '(7.5)? See graph

f'(1)=-1 f'(3)=0 f'(5)=1 f'(8)=0 f'(6.5) > f'(7.5) CLUE: f'(x) = slope