AP Calculus BC Semester 1 Review

Find the derivative of $f\left(x\right)\ =\ \tan\left(5x\right)^2$  

•  $f'\left(x\right)=10\tan\left(5x\right)$  

•  $f'\left(x\right)=10\sec^2\left(5x\right)\tan\left(5x\right)$  

•  $f'\left(x\right)=2\sec^2\left(x\right)\tan\left(x\right)$  

•  $f'\left(x\right)=10\sec^2\left(5x\right)$  

Given the point (0,2) occurs on the function f(x) = $e^x+\cos\left(x\right)$ , find the equation of the tangent line at that point. 

• y + 2 = x

• y = x + 2

• y = 2x

• y = 1/2x

Find the derivative with respect to x in the equation

 $y^3+y^2-5y-x^2=-4$  

•  $\frac{dy}{dx}=\frac{3y^2+2y-5}{2x}$  

•  $\frac{dy}{dx}=\frac{2x-4}{3y^2+2y-5}$  

•  $\frac{dy}{dx}=\frac{2}{3y+2}$  

•  $\frac{dy}{dx}=\frac{2x}{3y^2+2y-5}$  

Suppose the radius of a circle is expanding at 2 meters per second. At 3 seconds, what rate is the Area increasing by?

• $24\pi\ \frac{m}{s}$

• $24\pi\ \frac{m^2}{s}$

• $24\ \frac{m^2}{s}$

• $12\pi\ \frac{m}{s}$

• 4

• 0

• 8

• DNE

Using the Mean Value Theorem, at what x-value does instantaneous rate of change equal the average rate of change for the function $f\left(x\right)=x^4-8x$  over the interval [0,2]?

• 0

•  $2^3$  

•  $2^{\frac{1}{3}}$  

• DNE

Use the first derivative to determine the interval at which $f\left(x\right)=\left(x+2\right)^{\frac{2}{3}}$  is decreasing.

•  $\left(-\infty,\infty\right)$  

•  $\left(-\infty,-2\right]$  

•  $\left[-2,\infty\right)$  

• DNE

Given the the function $F\left(t\right)=10t^3-120t^2+450t+1000$  determine the absolute minimum value on the closed interval [0,8]

• 1000

• 1540

• 1500

• 2040

• 2.5

• 3.5

• 4.0

• 5.5
  

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