What is the extreme 9x^3-54x^2+81x+13 ?

The extreme 9x^3-54x^2+81x+13 is Maximum(1,49),Minimum(3,13)

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extreme 9x^3-54x^2+81x+13

extreme points

9 x^{3} - 54 x^{2} + 81 x + 13

Maximum (1, 49), Minimum (3, 13)

Solution steps

f^{'} (x) = 27 x^{2} - 108 x + 81

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 1

into

9 x^{3} - 54 x^{2} + 81 x + 13 : 49

Maximum (1, 49)

Plug

x = 3

into

9 x^{3} - 54 x^{2} + 81 x + 13 : 13

Minimum (3, 13)

Maximum (1, 49), Minimum (3, 13)

y + 3 x - 5 = 0

\frac{d}{x d x}

f (x) = 4 x^{4} - 8 x^{3} + 4

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

f (x) = 2 x^{2} + 8 x - 6

What is the extreme 9x^3-54x^2+81x+13 ?
The extreme 9x^3-54x^2+81x+13 is Maximum(1,49),Minimum(3,13)