2.16 Derivatives Test

Find the derivative.

• x⁴ cosx - 4x³sinx
• x⁴ cosx + 4x³sinx
• 4x³cosx
• -4x³cosx

Tags

CCSS.HSA.APR.A.1

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.TF.A.2

.

• (3x²-2)cos(x³-2x)

• -(3x²-2)cos(x³-2x)

• cos(2x²-2)

• sin(2x²-2)

Find h'(3)

• -2
• 0
• 1
• 3

Tags

CCSS.HSF.IF.A.2

The value of c guaranteed to exist by the MVT for  $f\left(x\right)=x^2$  on the interval [0,3] is:

• 1

• 2

• 3/2

• 1/2

 $f\left(x\right)=\left(x+3\right)\left(x-1\right)^2,\ \ \ \ \left[-3,1\right]$  

Find the value of c which is guaranteed by Rolle's Theorem.

• -1

• 5/3

• 3/5

• Rolle's Theorem doesn't apply

This is NOT a correct notation for a derivative

• y ' (say it as "y prime")

• f '(x) (say it as "f prime of x")

• dy/dx

• dx/dy

 $\lim_{x\rightarrow1}\ \frac{\sqrt{x^2+3x}-2}{x-1}$  is the instantaneous rate of change of what function at what value of the domain? 

•  $f\left(x\right)=\sqrt{x^2-3x}-2$  at  $x=1$  

•  $f\left(x\right)=\sqrt{x^2-3x}$  at  $x=2$  

•  $f\left(x\right)=\frac{\sqrt{x^2-3x}}{x-1}$  at  $x=1$  

•  $f\left(x\right)=\sqrt{x^2-3x}$  at  $x=1$  

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

f'(x)=

• $\lim_{h\rightarrow0}\left(\frac{f\left(x+h\right)-f\left(x\right)}{h}\right)$

• $\lim_{x\rightarrow c}\left(\frac{f\left(x\right)-f\left(c\right)}{x-c}\right)$

• $\frac{\text{d}y}{\text{d}x}$

• an equation for the slope of the tangent line

 $\frac{d}{dt}\left(4\sec t+\tan t\right)=$  

•  $4\tan t+\sec t$  

•  $4\sec t+\tan t$  

•  $\tan t\left(4\sec t+\tan t\right)$  

•  $\sec t\left(4\tan t+\sec t\right)$  

Tags

CCSS.HSF.TF.C.8

 $\frac{d}{dx}\left(\frac{\sin x}{1+\cos x}\right)=$  

•  $\frac{\cos x}{-\sin x}$  

•  $\frac{-\sin^2x-\cos x+\cos^2x}{\left(1+\cos x\right)^2}$  

•  $\frac{1}{1+\cos x}$  

•  $\frac{-\cos^2x+\cos x+\sin^2x}{\left(1+\cos x\right)^2}$  

Tags

CCSS.HSA.APR.D.7

CCSS.HSF.IF.C.8