Derivatives and Critical Points

Which one of the following statements is always true?

• When a graph is increasing, its derivative is negative.

• When a graph is decreasing, so is its derivative.

• When a graph is decreasing, its derivative is negative.

• When a graph is increasing, so is its derivative.

Tags

CCSS.HSF.IF.B.4

For a function g(x), g'(-2)=0 indicates that x=-2 is ________________.

• an inflection point
• a critical point
• a relative maximum
• a relative minimum

If given f'(x) how would you find the intervals which the graph f(x) has a positive slope( increasing)?

• f'(x) < 0 (negative)

• f'(x) > 0 (positive)

• f'(x) is increasing

• Can't be determined

When f'(x) changes from positive to negative, there is(are) ...

• a maximum.
• a minimum.
• no extrema.

f' is given, which could be f?

• A
• B
• C

Identify the critical points of the following function:
g(x)=2x³-3x²

• x=-1,1
• x=0,0
• x=0,-1
• x=0,1

What is the relative maximum value?

• y = 4
• y = 2
• y = 1
• y = -1

What is the derivative of ax?

• a
• x
• 1
• 0

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

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

When f'(x) changes from negative to positive, there is(are) ...

• a maximum.
• a minimum.
• no extrema.