Mathematics

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