Chapter 3 Test AP Calc

if  $x^2+y^2=a^2$  , where a is a constant, find  $\frac{d^2y}{dx^2}$  .

•  $\frac{-a^2}{y^3}$  

•  $\frac{x^2-y^2}{y^3}$  

•  $\frac{-y^2-x^2}{y^2}$  

•  $\frac{1}{a^2}$  

For the function $f$   ,  $f'\left(x\right)=4x-3$  and  $f\left(2\right)=4.\$  What is the approximation for  $f\left(2.1\right)$  found by using the tangent line to the graph of  $f$  at  $x=2.$  

• -2.6

• 4.5

• 4.8

• 5.4

Let  $f$  be a differentiable function such that  $f\left(-4\right)=12,\ f\left(9\right)=-4,\ f'\left(4\right)=-6,\ f'\left(9\right)=3.$  The function  $g$  is differentiable and  $g\left(x\right)=f^{-1}\left(x\right)$  for all x.  What is the value of  $g'\left(-4\right)?$  

•  $-\frac{1}{6}$  

•  $-\frac{1}{4}$  

•  $\frac{1}{3}$  

•  $\frac{1}{9}$  

Tags

CCSS.HSF-BF.B.4A

 $f\left(x\right)=\left(2x+1\right)\left(x^2-3\right)^4,\ then\ f;\left(x\right)=$  

if

•  $4\left(2x+1\right)\left(x^2-3\right)^3$  

•  $8x\left(2x+1\right)\left(x^2-3\right)^3$  

•  $2\left(x^2-3\right)^3\left(3x^2+x-3\right)$  

•  $2\left(x^2-3\right)^3\left(9x^2+4x-3\right)$  

• $\frac{2}{17}$

• $\frac{1}{17}$

• $-\frac{2}{15}$

• $-\frac{1}{15}$

• 1 and 5 only

• 2 only

• 1, 3, and 5 only

• 1, 3, 4, and 5 only

Tags

CCSS.HSF.IF.B.4

Find the equation of the tangent line to $x^3+y^3=3xy+5x-3y$  at (2, 2).

•  $y=\frac{-1}{9}\left(x-2\right)+2$  

•  $y=\frac{13}{3}\left(x-2\right)+2$  

•  $y=2$  

•  $y=\frac{1}{9}\left(x-2\right)+2$