Question

Find the point of Maxima of y = x3 - 18x2+96x​

Answer 1

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Refer to the attachment

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

f(x) = x³ – 18x² +96x -

f'(x) = 3x² − 36x +96

f'(x) = x² - 12x + 32 = 0

=x²- 8x - 4x +32 = 0

= x(x − 8) − 4(x − 8)

-

-

f'(x) = (x − 4) (x − 8) = 0

-

x = 4,8

f'(x) = 2x - 12

f'(4) = −4 <0

x = 4 point of maxima

f(4) = 64 16 × 18 + 96 × 4

= 448 288 = 160