Mac review 1

a)Graph the function f(x)=2x^2-7x+5 b)Draw a tangent line to the graph at the point whose​ x-coordinate is 3. c)Find f'(x) by determining lim h-->0 f(x+h)-f(x)/h d)Find f'(3).

a) Factor the equation, which gives you x coordinates for the graph. first number positive means cup. b)Just find graph that copies previous and with an x-coordinate of 3 c) Use definition to derive d) plug in 3 to the derivative

a)Use the product rule to find the derivative of the given function. b) Find the derivative by expanding the product first. h(z)=(5-z^2)(z^3-2z+4)

a)(5-z^2)(3x^2-2)+(z^3-2z+4)(-2z) Look for an answer with four options and set up a normal HidLo + LodHi with it b) -z^5+7z^3-4z^2-10z+20 then differentiate -5z^4+21z^2-8z-10

a) Use the Product Rule to find the derivative of the given function. ​b) Find the derivative by multiplying the expressions first. y=(9(sqrootx)+8)x^2

a)(9(sqrootx)+8)(2x)+(x^2)(9/2 x^-.5) look for one with four and do hidlo+lodhi b) 9x^5/2 + 8x^2 multiply what they give you and simplify then differentiate 45/2 x^3/2 +16x

lim x-->5 g(x)

the limit does not exist because there are holes

Differentiate the function. y=sqroot of x^2 +12

x/sqroot of x^2+12 change it to (x^2+12)^.5 then simplify

Differentiate the given function. y=x(x^5+1)^3

(x^5+1)^2(16x^5+1) Product Rule and simplify

Find an equation for the tangent line to the graph of f(x)=x^2 - 7 at (−5,18).

-10x-32 differentiate the function y'=2x m=2(-5)=-10 y-y1=m(x-x1) y-18=-10(x+5) -10x-32

Differentiate using the definition but NOT the lim--> 0 part, leave h in f(x)=2/x+2

-2/(x+h+2)(x+2) differentiate using the definition and just leave h

Differentiate using the definition. f(x)=-x^2-4x-3

-2x-4-h leave in the h if it doesn't say lim-->0

Find the derivative of y=-6x^6

-36x^5

differentiate y=7x^-6

-42x^-7 Just use power rule like normal

Find the derivative of the function y=sqroot of 9-5x

-5/2sqroot of 9-5x Change the equation to (9-5x)^.5 then use chain rule

lim x-->-3 x^2-9/x+3

-6 =(x+3)(x-3)/x+3 =x-3 =(-3)-3 =-6

Find the 2nd derivative of y=-2x^6-7

-60x^4

Differentiate the function. y=9x^2-2/7x^3+4

-63x^4+42x^2+72x Use quotient rule and don't simplify bottom LodHi-HidLo/Lo^2

differentiate y=8

0

Consider the function f and its graph given to the right. lim x-->2

1

Find a simplified form of the difference quotient and​ (b) complete the following table. f(x)=-2x+5

y'=-2 Differentiate the equation.

Differentiate the function. y=(6x^4−x+3)(−x^5+3)

y'=-54x^8 + 6^5 - 15x^4 + 72x^3 - 3 Use Product Rule (HiDLo+LoDHi)

Find the given limit. lim x-->3 (-x^2+9x-8)

10 plug in 3

Find the derivative of x^12

12x^11

Find f'(4) if f(x)=4x^3

192

lim x--> -1 (7x+9)

2 plug in -1 to x -7+9=2

Find 2nd derivative. y=7x^5/5 -2x

28x^3 separate 7/5 and multiply later differentiate x^5 twice 5x^4, then 20x^3 multiply this by 7/5 and simplify

Find a simplified form of the difference quotient and​ (b) complete the following table. f(x)=2x^2

4x+2h differentiate using the definition

Lim f(x) X--> -7-

5, both meet from left and right at y=5

find the 2nd derivative. y=1/x^7

56x^-9 change to x^-7 and then differentiate

Find the given limit. lim x-->-8 x^2-1/8-x

63/16 plug in -8

lim f(x) x-->2

7 As x approaches 2 from the left and right the y- coordinate is 7

Find the 2nd derivative of f(x)= 4x^2-15x-7/x^3

8-84/x^5 differentiate first two things normally -15x=0 and 4x^2=8 change to -7x^-3 so it would end up 21x^-4 then -84x^-5 and then flip so its 8-84/x^5

Using the definition find f'(6) f(x)=8x^2

96

Differentiate the function. f(x)=(3+x^3)^3 - (8+x^5)^4

9x^2(3+x^3)^2-20x^4(8+x^5)^3 Use chain rule for each individual sections and the combine and simplify