Question

Determine the maximum and minimum values of the function
f(x) = x5 - 5x4 + 5x3 - 1
​

Answer 1

Explanation:

f(x)=x

5

−5x

4

+5x

3

−1

f

′

(x)=5x

4

−20x

3

+15x

2

=5x

2

(x−1)(x−3)=0

⇒x=0,1,3

f

′′

(x)=10x(2x

2

−6x+3)

now, f

′′

(0)=0

and f

′′

(1)=10(2−6+3)<0

and f

′′

(3)=10(18−12+3)>0

Therefore, f(x) is minimum at x=3 and maximum at x=1

Ans: D