11 Calculus Derivatives

Question 1

Find the anti-derivative of f'\left(x\right)=3x^2-4x given that f\left(1\right)=2

Accepted Answer

x^3-2x^2+3

Question 2

For the function f\left(x\right)=x^3-2x^2+2, find the equation of the normal at the point where x=2

Accepted Answer

y=-\frac{1}{4}x+\frac{5}{2}

Question 3

Find the average rate of change of f\left(x\right)=-\frac{1}{2}x^3+2x^2-3x between x=0 and x=2

Accepted Answer

-1

Question 4

What is the slope of the tangent line to f\left(x\right)=2x^2-5x at x=1

Accepted Answer

-1

Question 5

Evaluate the limit: \lim_{x	o-3}\frac{x^2-1}{x+1}

Accepted Answer

-4

Question 6

Find f′(4) given that f\left(x\right)=\frac{1}{2}x^4+x^3+2

Accepted Answer

176

Question 7

Find f''\left(x\right) for f\left(x\right)=x^3-3x^2+2x

Accepted Answer

6x-6

Question 8

Evaluate the limit: \lim_{x	o-4}\frac{2x^2+3x-20}{x+4}

Accepted Answer

-13

Question 9

Find f(x) if f'\left(x\right)=4x^3-2x+5

Accepted Answer

x^4-x^2+5x+c

Question 10

Evaluate f'(9) for f\left(x\right)=4x^{\frac{3}{2}}-5x^2

Accepted Answer

-72

Question 11

What is the derivative of f\left(x\right)=3x^2+2x-5

Accepted Answer

6x+2

Question 12

What is the equation of the tangent line to f\left(x\right)=x^3 at x=1?

Accepted Answer

y=3x-2

Question 13

For the function f\left(x\right)=2x^2+3x-5, find the equation of the tangent at the point where x=1

Accepted Answer

y=7x-7

Question 14

Find the equation of the tangent line at x=1 for f\left(x\right)=x^4-4x^3+6

Accepted Answer

y=-8x+11

Question 15

Find the anti-derivative of f\left(x\right)=2x^3-5x+7 given that F(0)=3

Accepted Answer

F\left(x\right)=\frac{1}{2}x^4-\frac{5}{2}x^2+7x+3

Question 16

If graph of f(x) has a turning point at x=2, what is the value of the derivative at that point?

Accepted Answer

0

Question 17

Evaluate the limit: \lim_{x	o2}\frac{3x^2-10x+8}{x-2}

Accepted Answer

2

Questions 17