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