Using the First Derivative Test to Find Relative (Local) Extrema Quiz (MCQs)

The function f is defined by f(x)=x^2e^-x^2. At what values of x does f have a relative maximum?

-1 and 1

Let f be the function with derivative f'(x)=x^3-3x-2

f has one relative minimum and no relative maxima

Let f be the function with derivative f'(x)=x^3-3x+2. Which of the following statements is true?

f has one relative minimum and no relative maxima.

Let f be a differentiable function with a domain of (0,10). It is known that f′⁡(x), the derivative of f⁡(x), is negative on the intervals (0,2) and (4,6) and positive on the intervals (2,4) and (6,10). Which of the following statements is true?

f has two relative minima and one relative maximum.

Let f be a differentiable function with a domain of (0,5). It is known that f′⁡(x), the derivative of f⁡(x), is negative on the intervals (0,1) and (2,3) and positive on the intervals (1,2) and (3,5). Which of the following statements is true?

f has two relative minima and one relative maximum.

The function f is defined by f(x)=e^-x(x^2+2x). At what values of x does f have a relative maximum?

x=√2 only