Calculus BC Practice Problems- MC

If n is a positive integer, the function

 $f\left(x\right)=x^2+5\cos x$  will have how many points of inflection over the interval  $\left[0,2\pi n\right]$  ?

• 2

•  $2\pi$  

•  $n$  

•  $2n$  

If  $y^2-2xy=21$  , then  $\frac{dy}{dx}$  at the point  $\left(2,-3\right)$  is

•  $\frac{6}{5}$  

•  $\frac{3}{5}$  

•  $-\frac{2}{5}$  

•  $-\frac{3}{5}$  

A particle moves in the xy-plane so that its position at any time is given by  $x\left(t\right)=4\sin\left(\pi t\right)$  and  $y\left(t\right)=\left(3t-1\right)^2$  .  What is the speed of the particle at  $t=2$  ?

• 13.708

• 30.209

• 32.526

• 42.566

The second derivative of a function is given by $f''\left(x\right)=0.5+\cos\left(x\right)-e^{-x}$ .  Over the interval  $\left[-2,4\right]$  the graph of the function  $f$  changes from concave up to concave down at approximately  $x=$  

• -0.36

• 0.59

• 1.93

• 3.10

A particle moving along a curve in the xy-plane has a position vector given by $\left(\frac{t^4}{4},\sin\left(t\right)\right)$ .  What is the total distance the particle travels between  $t=0$  and  $t=\pi$  ? 

• 25.7

• 25.1

• 7.6

• 7.7

If $\int_2^xf\left(t\right)dt=\frac{6x}{\sqrt{9x^2-20}}-3$ , then  $\int_2^{\infty}f\left(t\right)dt$  is

• divergent

• -3

• 0

• -1

Let $f\left(x\right)=x^3-7x^2+25x-39$  and let  $g$  be the inverse function of  $f$  .  What is the value of  $g'\left(0\right)$  ?

• 25

• 10

•  $\frac{1}{25}$  

•  $\frac{1}{10}$  
  

Oil flows into a concrete conical storage pit at the rate of 10 cubic feet per minute. The pit was built point down and has a depth of 15 feet and a ground level radius of 9 feet. How fast, in feet per minute, is the oil level rising when the oil is 10 feet deep?

• 0.05

• 0.09

• 0.13

• 0.44

Let  $f$  be the function defined above, where  $a$  and  $b$  are constants.  If  $f$  is differentiable at  $x=0$ , what is the value of  $a+b$  ?

• -3

• -2

• 0

• 2

Let $f$ be a function whose derivative is given by  $f'\left(x\right)=\frac{x}{15}+\sin\left(e^{0.2x}\right)$  .  Which of the following is the approximate  $x-$ value of a relative maximum point on the graph of  $f$  ?

• 2.830

• 6.378

• 8.673

• 10.332