Review For Quiz Differentiability and Power Rule

Assume h> 0

What is:

 $\lim_{h\rightarrow0}\ \frac{f\left(a-h\right)-f\left(a\right)}{h}$  ?

• The average rate of change

• The Left Hand Derivative at x = a

• The Right Hand Derivative at x = a

• An indication that the slope at x = a is zero. 

Assume h> 0

What is:

 $\lim_{h\rightarrow0}\ \frac{f\left(a+h\right)-f\left(a\right)}{h}$  ?

• The average rate of change

• The Left Hand Derivative at x = a

• The Right Hand Derivative at x = a

• An indication that the slope at x = a is zero. 

Find the derivative of the given equation
f(x) = x³ + x² + 3

• 3x² + 2x
• 3x + 2x 
• 3x + 2x + 3
• x³ + x² 

Tags

CCSS.HSA.APR.A.1

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

• m = 0
• f'(x) = -6x - 6
• f'(x) = 6x
• m = -12

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

• 7
• 0
• 7x
• 14

Find the derivative of y=5x⁴

• (5x³)/4
• 20x⁴
• 20x³
• x⁵

What is the derivative of xⁿ?

• (n-1)xⁿ
• nxⁿ⁺¹
• (n+1)x^n-1
• nx^n-1

What is the equation of the line tangent to the curve y = x² at x = 1?

• y = 2x + 1

• y = 2x - 1

• y = -2x + 1

• y = x - 1

Tags

CCSS.HSA.REI.C.7

CCSS.HSG.GPE.B.5

What is the equation of the line tangent to f(x)= 4x²+2x-1 at x=0?

• y+1=2(x+1)

• y=2x-1

• y=2x+2

• y= -x-1

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.B.3

When we "take the derivative" of a function what are we finding?

• What's a derivative?
• The rate at which our struggles in Calculus are increasing.
• The slope of the secant line
• The slope of the tangent line