Derivatives and Limit Review - SHS

Find the derivative of the given function at the indicated value.
 $f\left(x\right)\ =\ \frac{-9}{x},\ at\ x=-11$  

• 9/11

• 11/9

• 121/9

• 9/121

• none of these

Find the derivative of the given function at the given value.
 $f\left(x\right)=x^3+6,\ at\ x=2$  

• -12

• 13

• 18

• 12

• none of these

Find the slope of the line tangent to the curve at the given x value.
 $y=x^2-9x,\ at\ x=-5$  

• 70

• -10

• -19

• 35

• none of these

If  $y=x^2+3$  , find an equation of the tangent to the graph of y at x = 4.

• y = 8x - 13

• y = 8x -29

• y = 4x - 13

• y = 8x - 26

• none of these

Find an equation of the tangent line to the graph of  $y=x-x^2$  at the point (-2, -6). 

• y = -3x - 4

• y = 5x + 4

• y = -3x + 4

• y = -5x + 4

• none of these

Find the equation of the normal line to the curve  $y=3x-5x^2$  at the point (-3, -54)

• x - 27y + 975 = 0

• x + 33y + 1785 = 0

• x - 27y + 1785 = 0

• 33x - y + 45 = 0

• none of these

Find the derivative of  $y=24-3x$  

• 24 - 3x

• -3x

• -3

• 21

• none of these

Find the derivative of:  $f\left(x\right)=x^2-1$  

• x - 1
  

• 2x - 1

• 2x

•  $2x^2$  

• none of these

Find $\frac{dy}{dx}$  .   $y=\frac{1}{\sqrt{7-4x}}$  

•  $-\frac{2}{\sqrt{7-4x}}$  

•  $-\frac{1}{2\left(7-4x\right)^{\frac{3}{2}}}$ 

•  $\frac{1}{2}\sqrt{7-4x}$  

•  $\frac{2}{\left(7-4x\right)^{\frac{3}{2}}}$  

• none of these

Find $\frac{dy}{dx}$ .    $y=\sqrt{19x-x^7}$  

•  $\frac{19-7x^6}{2\sqrt{19x-x^7}}$  

•  $\frac{1}{2\sqrt{19x-x^7}}$  

•  $\frac{-7x^6}{2\sqrt{19x-x^7}}$  

•  $\frac{1}{2\sqrt{19-x^6}}$  

• none of these