Question

Find Maximum and Minimum value of x³ - 18x² + 98x ?​

Answer 1

Step-by-step explanation:

Answer

(d) Let y=x

3

−18x

2

+96x,xϵ[0,9]

dx

dy

=3x

2

−36x+96

⇒

dx

dy

=3(x

2

−12x+32)

⇒

dx

dy

=3(x−8)(x−4)

For maxima or minima

dx

dy

=0

⇒3(x−8)(x−4)=0

x=4,8

y

0

=(0)

3

−18(0)

2

+96(0)

⇒y

0

=0

y

4

=(0)

3

−15(0)

2

+96(0)

=64−288+384=160

y

8

=(8)

3

−18(8)

2

+96×8

=512−1152+768

=128

y

9

=(9)

3

−18(9)

2

+96(9)

=729−1458+864=135

So, at x=0 minimum value =0

and at $x=4 maximum value =160