Determine Maximum and Minimums of Functions

Does this function have a minimum, maximum, both or neither?

• Minimum

• Maximum

• Both

• Neither

If a function has a second derivative that is negative, what does that tell you?

• The function is increasing
• The function is decreasing
• The function is concave up
• The function is concave down

If a function has a second derivative that is positive, what does that tell you?

• The function is increasing
• The function is decreasing
• The function is concave up
• The function is concave down

What is a point of inflection?

• When a function goes from increasing to decreasing
• When a function goes from concave up to concave down

The slope of a function is described by its ____________.

• first derivative
• second derivative
• third derivative
• expression

Does this graph have a maximum or minimum value?

• maximum
• minimum
• neither
• both

Does
y = -4x²
have a maximum or minimum value?

• maximum
• minimum
• both
• neither

Find the x-coordinate of the inflection point of f(x)=6x²-x³.

• -2
• 0
• 2
• None

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

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

Identify the relative maximum:

• (0, 3)
• (4, 1)
• (3, 0)
• (1, 4)