Critical Points

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

• decreasing
• increasing
• concave up
• concave down

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

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

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

Find the critical points of f(x) = 2x⁴- 4x² + 1

• x= 0
• x = -1, 1
• x = -1, 0, 1
• no critical points

Tags

CCSS.HSA.APR.B.3

Derivative means the same thing as

• slope of the tangent line
• slope of the normal line
• exponent
• potato

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