Derivatives Review

Find the slope of the tangent line to the graph of f at x=4 given that

 $f\left(x\right)=-x^2+4\sqrt{x}$  

• -8

• -12

• -9

• -7

Find the instantaneous rate of change of

 $f\left(x\right)=\left(2x^3-3x+4\right)\sqrt{x^2+3x+4}$  at x=0

• 3

•  $-\frac{3}{4}$  

• 0

• -3

An equation of the line tangent to the graph of

 $3y^2-x^3-xy^2=7$  at the point (1, 2) is

•  $y=\frac{3}{4}x-\frac{3}{8}$  

•  $y=\frac{3}{4}x+\frac{1}{2}$  

•  $y=-\frac{7}{8}x+\frac{3}{2}$  

•  $y=\frac{7}{8}x+\frac{9}{8}$  

Consider the curve

 $x^2+6y-3xy=7$  . Find the x-coordinate of each place where the tangent line is vertical.

• x=2

• x=-2

• Undefined

•  $x=\frac{1}{2}$  

The equation of the tangent line of

 $y=x\sqrt{3+x^2}$  at the point (1, 2) is

•  $y=\frac{3}{2}x-\frac{1}{2}$  

•  $y=\frac{1}{2}x+\frac{1}{2}$  

•  $y=\frac{5}{2}x+\frac{1}{2}$  

•  $y=\frac{5}{2}x-\frac{1}{2}$  

Given the table, calculate h'(1) if h(x)=f(g(x))

• h'(1)=-1

• h'(1)=1

• h'(1)=-2

• h'(1)=-3

Given the table, calculate h'(1) if h(x)=f(x)g(x)

• h'(1)=-1

• h'(1)=2

• h'(1)=-2

• h'(1)=-3

Given the table, calculate h'(2) if  $h(x)=xf(x^2)$  

• h'(2)=13

• h'(2)=8

• h'(2)=10

• h'(2)=7

Determine a and b such that f(x) is differentiable at x=1

• a=4, b=2

• a=3, b=1

• a=1, b=0

• $a=\frac{5}{3},\ b=\frac{1}{3}$

• A

• B

• C

• D