Maxima and Minima of Graphs of Polynomials

• False

• True

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

• maximum

• minimum

• both

• neither

Tags

CCSS.HSF-IF.C.7A

Which of the following statements is true?

• (a) The absolute minimum of a function can occur at an endpoint.

• (b) The absolute minimum of a function cannot be a local minimum.

• (c) A local maximum can occur at an endpoint.

If f ′(c) = 0 , then

• (a) f has a local maximum or local minimum at c.

• (b) f has an absolute maximum or minimum at c.

• (c) c is a candidate for a local extreme point.

If f '(3) = 0 and f"(3) < 0, then which of the following must be true?

• There is a local max at x=3

• There is a local min at x = 3

• There is an inflection point at x = 3

• There is an x-intercept at x = 3

What is the maximum value of f(x) = x³ - 3x² - 1 on the interval [-3, 2]?

• 0

• -1

• 2

• 5

Match the graph to the function

• f(x) = -2x⁶+9x²

• f(x) = x⁴+x³-5x²-6

• f(x) = -½x⁴+1

• f(x) = -x²+3x

What is the leading coefficient?

• Positive 

• Negative

• Odd 

• Even

Match the graph to the function

• f(x) = -2x⁶+9x²

• f(x) = x⁶-7x⁴+12x²-x-2

• f(x) = x⁶-3x³+x+2

• f(x) = -x⁶+5x⁴+3x-2