Derivatives A

Find the derivative of the given equation
f(x) = 7

• 7
• 0
• 7x
• 14

If a function has a derivative that is negative, what does that tell you?

• The function is increasing
• The function is decreasing

Tags

CCSS.HSF.IF.B.4

Given a function, f(x), if f'(x)>0 over a certain interval, then f(x) is __________ over that interval.

• increasing
• decreasing
• concave up
• concave down

Find the second derivative of the function:
f (x) =  2x - 5x⁶

• f ''(x)= 2 - 30x
• f ''(x) =  2-30x⁵
• f ''(x) = -30x⁵
• f ''(x) = -150x⁴

Tags

CCSS.HSA.APR.A.1

At which point(s) will the slope of the tangent line be zero?

• at C only

• at points A, C and E only

• at point B and D only

• at points A and E only

What is the slope of the line normal to the curve y = x² + x at x = 1?

• -1

• -1/2

• -1/3

• -1/4

Tags

CCSS.HSG.GPE.B.5

The tangent line to f(x)=x³+kx² at x = 1 is parallel to the line containing points (2, 9) and (3, 10).  What is the value of k?

• -2
• -1
• 1
• 2

Tags

CCSS.HSG.GPE.B.5

Find the derivative of
 $g\left(x\right)=\frac{3x-2}{x^2+2}$  

•  $\frac{3}{2x}$  
  

•  $\frac{3\left(x^2+2\right)}{\left(x^2+2\right)^2}$  

•  $\frac{-3x^2+4x+6}{\left(x^2+2\right)^2}$  
  

•  $\frac{9x^2-4x+6}{\left(x^2+2\right)^2}$  
  

Tags

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

The position of an object is given as a function of time by x = 3t² + 5t³ - 2t
What is the acceleration of the object at time t = 2 s?

• 64 m/s/s
• 60 m/s/s
• 66 m/s/s
• 70 m/s/s

Tags

CCSS.HSF.IF.A.2

The velocity of an object is given as v = 2t + 3t³. what is the acceleration of the object at t = 2 s?

• 38 m/s/s
• 27 m/s/s
• 16 m/s/s
• 49 m/s/s

Tags

CCSS.HSA.SSE.A.1

CCSS.HSN.VM.A.3