extreme values

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

Given a function g(x), if g'(x)=0 at a certain value of x, then g(x) has _____________ at x.

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

For a function f(x), f''(4)=0 indicates that x=4 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

The concavity of a function is described by its _______________.

• first derivative
• second derivative
• third derivative
• expression

f''(x) is pictured. Over which interval is f(x) concave up? (Be careful - this is a second derivative graph!)

• (-infinity, 3)

• (-5, -1)

• nowhere

• (0, 4)

f''(x) is pictured. Which x values are inflection points of f(x)? (Be careful - this is a second derivative graph!)

• x=-5 and -1

• x=-3

• x=4

• no inflection points

Identify the interval from the derivative graph where the function is concave up.

• (-1,1) & (3,4)
• (-3,-2)
• (-2,-1)
• (-3,-1) & (1,3)

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Find the relative minimum values for f(x)=3x⁴-2x³-9x²

• -1

• 0

• 1.5

• -1 and 1.5

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSA.APR.B.3