Calc Review 12/17

For some function f(x):

f(3) = 5 and f '(3) = -2.

Use the tangent line at x = 3 to approximate the value of f(3.1).

• 5.01

• 4.98

• 5.2

• 4.8

• 5.02

For

 $\sin\left(y^2\right)=x^3-5$  , find  $\frac{dy}{dx}$  .

•  $\frac{dy}{dx}=\frac{3x^2}{\cos\left(y^2\right)}$  

•  $\frac{dy}{dx}=-\frac{3x^2}{\cos\left(y^2\right)}$  

•  $\frac{dy}{dx}=\frac{3x^2}{2y\cos\left(y^2\right)}$  

•  $\frac{dy}{dx}=-\frac{3x^2}{2y\cos\left(y^2\right)}$  

Write the equation of the line tangent to  $f\left(x\right)=\ln\left(x^2-1\right)$  at x = 3.

•  $y+\ln8=\frac{3}{4}\left(x-3\right)$  

•  $y-\ln8=\frac{2}{3}\left(x-3\right)$  

•  $y-\ln8=\frac{1}{8}\left(x-3\right)$  

•  $y-3\ln2=\frac{3}{4}\left(x-3\right)$  

If  $f'\left(c\right)=0$   and  $f'$  changes from negative to positive at x = c, then at x = c, f has a:

• relative maximum

• relative minimum

• point of inflection

• Not enough info to conclude

For functions f and g ,  $f\left(x\right)=g^{-1}\left(x\right)$ .  

If  f(6) = 5,  $f'\left(6\right)=-\frac{1}{5}$  , f(-2) = 6, and  $f'\left(-2\right)=7$  , write the equation of the line tangent to g(x) at x = 6.

•  $y-5=-5\left(x-6\right)$  

•  $y-5=5\left(x-6\right)$  

•  $y+2=\frac{1}{7}\left(x-6\right)$  

•  $y+2=-\frac{1}{7}\left(x-6\right)$