Show solutions AP Calculus Test1

Find the slope of the tangent line to f(x) = -3x²-6x at x = 1.

• m = 0
• m = 12
• m = -9
• m = -12

Tags

CCSS.8.EE.B.5

Find the derivative f(x) = (x² + 2x)⁵

• f'(x) = 5(2x+2)⁴
• f'(x) = 5(x² + 2x)⁴
•  f'(x) = 5(x² + 2x)⁴(2x)
• f'(x) = 5(x² + 2x)⁴(2x + 2)

If  $x^2\ +\ xy\ =\ 10,\$ then when x = 2,  $\frac{\text{d}y}{\text{d}x}$   is

• A      $-\frac{7}{2}$  

• B      $\frac{7}{2}$  

• C      $\frac{2}{7}$  

• D        $-\frac{2}{7}$  

f(x)=(sin²x), f'(x)= ?

• 2sin x
• 2(sin x)(cos x)
• 2cos x
• 2x(cos x)

Tags

CCSS.HSF.TF.C.9

What is y' if  $y\ =\ \sin\left(x^3-2x\right)$  

• (3x²-2) cos(x³-2x)

• -(3x²-2) cos(x³-2x)

• cos(2x²-2)

• sin(2x²-2)

What is the speed of the position function f(x)=-3x²-6x-6 at x=2 (speed is the absolute value of velocity)

• -18

• 18

• -6

• 6

The radius of a circle is decreasing at a constant rate of .1 centimeters per second. In terms of the circumference C, what is the rate of change of the area of the circle, in square centimeters per second?

• (0.2)πC

• -(.1)C

• $\frac{\ \ \left(.1\right)C}{2\pi}$

• $\left(.1\right)^2C$

• $\left(.1\right)^2\pi C$

Let f be the function defined by f(x)=4x³-10x+5. Find the equation of the tangent line to the graph of f at the point where x = 1

• y+1=2(x-1)

• y-1=2(x-1)

• y+1=2(x+1)

• y+1=-2(x-1)

Find v'(t) for v(t) =  $\ln\left(t^2+3\right)$  

• A.   $\frac{1}{t^2+3}$  

• B.   $e^{t^2}+3$  

• C.  $\frac{2t}{t^2+3}$  

• D.   $\ln\ 2t$  

• E.  none of the above

 $Find\ \ y'\ if\ y\ =\ 4x\ln\left(5x^4\right)$  

• A.   $4\ln\left(5x^4\right)$  

• B.   $16x\ +\ \ln\left(5x^4\right)$  

• C.   $20x^3+\frac{1}{5x^4}$  

• D.   $16\ +\ 4\ln\left(5x^4\right)$  

• E.  None of the above