Question 1

Find the derivative of $f(x)=2x^3+9x^2-x+4$.

Accepted Answer

$f'(x)=6x^2+18x-1$

Answer

$f'(x)=6x^2+18x$

Answer

$f'(x)=6x^2+18x+4$

Answer

$f'(x)=6x^2+18x-x$

Question 2

Find the derivative of $f(x)=\frac{6}{x^3}$.

Accepted Answer

$f'(x)=-\frac{18}{x^4}$

Answer

$f'(x)=-\frac{18}{x^5}$

Answer

$f'(x)=\frac{18}{x^5}$

Answer

$f'(x)=\frac{18}{x^4}$

Question 3

Find the derivative of $f(x)=6$.

Accepted Answer

$f'(x)=0$

Answer

$f'(x)=1$

Answer

$f'(x)=6$

Answer

$f'(x)=-6$

Question 4

Find the derivative of $f(x)=\sqrt x$.

Accepted Answer

$f'(x)=\frac{1}{2\sqrt x}$

Answer

$f'(x)=-\frac{1}{2\sqrt x}$

Answer

$f'(x)=\frac{\sqrt x}{2}$

Answer

$f'(x)=-\frac{\sqrt x}{2}$

Question 5

Find the derivative of $f(x)=12(\sqrt[4]{x})$.

Accepted Answer

$f'(x)=\frac{3}{\sqrt[4]{x^3}}$

Answer

$f'(x)=-\frac{3}{\sqrt[4]{x^3}}$

Answer

$f'(x)=\frac{3}{\sqrt[4]{x}}$

Answer

$f'(x)=-\frac{3}{\sqrt[4]{x}}$

Question 6

What is the equation of the line tangent to $f(x)=\frac12x^2-5x+1$ where $x=-2$?

Accepted Answer

$y=-7x-1$

Answer

$y=-5x+3$

Answer

$y=-7x+1$

Answer

$y=-7x+5$

Question 7

What is the equation of the line tangent to $f(x)=6\sqrt{x}$ where $x=4$?

Accepted Answer

$y=\frac32x+6$

Answer

$y=\frac32x-12$

Answer

$y=3x-24$

Answer

$y=3x$

Question 8

At which x-value(s) is the tangent to the graph of $f(x)=6x^2-3x+2$ horizontal?

Accepted Answer

$\frac14$

Answer

$-4$

Answer

$4$

Answer

$-\frac14$

Question 9

At which x-value(s) is the tangent to the graph of $f(x)=x^3-48x+1$ horizontal?

Accepted Answer

$-4$ and $4$

Answer

$4$

Answer

$0$

Answer

$-4$

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