Maxima and Minima of Polynomials

The function f(x) is said to have attained its maximum value for x=a if the function ceases to increase and begins to decrease at x= a

• False

• True

The function is said to have attained its minimum value for x=b if the function ceases to decrease and begins to increase at x=b

• True

• False

The maximum or minimum point are called the turning or stationary point.

• True

• False

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

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

For what values of x does the graph of g have a point of inflection f(x) = x⁴ + 4x³ - 18x² ?

• x = 4 and x = -1

• x = -4 and x = 1

• x = -3 and x = 1

• x = 3 and x = -1

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.