Let . The function has stationary points at and . Which of the following statements…

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let

f(x)=x^{3}-6x^{2}+9x+5

. The function has stationary points at

x=1

and

x=3

. Which of the following statements is true? (a)

x=1

is a local minimum and

x=3

is a local maximum (b) Both

x=1

and

x=3

are local minima (c)

x=1

is a local maximum and

x=3

is a local minimum (d) The second derivative test is inconclusive at both points