Maxima and Minima of Polynomials

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

• True

• False

For maximum point (i) ,\frac{\text{d}x}{\text{d}y}=0 ,(ii) \frac{\text{d}x}{\text{d}y} changes sign from +ve to -ve.

• False

• True

• False

• True

• False

• True

• False

• True

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

• maximum

• minimum

• both

• neither

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

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.