Calc 3.1 - 3.3 Review

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

• x=-1,1
• x=0,0
• x=0,-1
• x=0,1

Tags

CCSS.HSA.APR.B.3

Identify the interval(s) of decrease.

• 2<x<-3, 1<x<-1
• x<-3, -1<x<2, x>4
• -3<x<4
• -3<x<-1, 2<x<4

Identify the any local maximums for the following function:
g(x)=2x³-3x²

• (0, 0)
• (1, -1)
• (-1, -5)
• (0, 1) 

Let y=6x⁴-12x²-14.  Identify the critical points.  

• x=0,1,2
• x=-2,0,1
• x=0,1
• x=-1,0,1

Let h(x)=2x³-15x². Find the coordinates of the minimum point.

• (0,0)
• (5,-125)
• (0,7.5)
• (5,-25)

What are the intervals of the graph increasing for f(x) = 2x⁴- 4x² + 1

• (-1,0)
• (0,1)
• (-∞,-1) and (1,∞)
• (0,1) and (-1,0)

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

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

• f'(x) < 0 (negative)
• f'(x) > 0 (positive)
• f'(x) is increasing
• Can't be determined

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

Tags

CCSS.HSF.IF.B.6

CCSS.HSS.ID.C.7

How do you find the critical numbers of a function?

• Critical numbers only occur when f'(x) = 0.

• Critical numbers only occur when f'(x) is undefined.

• Critical numbers occur when f'(x) = 0 or where f'(x) is undefined.

• Critical numbers occur as x-intercepts on the graph.

For a function f(x), f'(-3) = 5 indicates f(x) is ___________ at x=-3.

• increasing
• decreasing
• concave up
• concave down