Question 1

Find the Equation of the Line Tangent to $y=x^3-3x^2+2$ at $(3,2)$

Accepted Answer

$y=9x-25$

Answer

$y=9x-15$

Answer

$y=3x-25$

Answer

$y=9x+25$

Question 2

Find the points where the tangent line to $y=\frac{1}{x^2-1}$ is Horizontal.

Accepted Answer

(0,-1)

Answer

(-1,0)

Answer

(0,1)

Answer

(-1,-1)

Question 3

For a function $f$, we are given that $f(8)=1$ and $f´(8)=2$. What is the equation of the line tangent to $f$ and $x=8$?

Accepted Answer

$y-1=2(x-8)$

Answer

$y-2=2(x-4)$

Answer

$y-8=2(x-8)$

Answer

$y-1=1(x-8)$

Question 4

Find the Equation of the Line Tangent to $y=(5x+5)^\frac{1}{2}$ at $(4,5)$.

Accepted Answer

$y=\frac{1}{2}x+3$

Answer

$y=\frac{1}{2}x-3$

Answer

$y=\frac{-1}{4}x+3$

Answer

$y=\frac{-1}{2}x +3$

Question 5

The Tangent line to the graph of the function $f$ at the point $(-1,5)$ and passes through the point $(-7,7)$. Find $f'(-1)$.

Accepted Answer

$\frac{-1}{3}$

Answer

$\frac{1}{3}$

Answer

$\frac{1}{2}$

Answer

$-3$

Question 6

For a function $h$, we are given that $h(-2)=-5$ and $h'(-2)=-9$. Whats the equation of the line tangent to the graph of$h$ at $x=-2$?

Accepted Answer

$y+5=-9(x+2)$

Answer

$y+2=-5(x+9)$

Answer

$y+2=9(x+5)$

Answer

$y+9=-5(x-2)$

Question 7

The tangent line to the graph of function $f$ at the point $(5,-7)$ passes through the point $(1,-1)$. Find $f'(5)$.

Accepted Answer

$\frac{-3}{2}$

Answer

$\frac{2}{3}$

Answer

$\frac{3}{2}$

Answer

$\frac{-2}{3}$

Question 8

For a function $h$, we are given that $h(-4)=7$ and $h'(-4)=1$. Whats the equation of the line tangent  to the graph of $h$ at$ x=-4$?

Accepted Answer

$y-7=1(x+4)$

Answer

$y+4=1(x-7)$

Answer

$y+4=7(x+4)$

Answer

$y-1=7(x+4)$

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