What is the extreme f(x)=2x^3-12x^2+18x+5 ?

The extreme f(x)=2x^3-12x^2+18x+5 is Maximum(1,13),Minimum(3,5)

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extreme f(x)=2x^3-12x^2+18x+5

extreme points

f (x) = 2 x^{3} - 12 x^{2} + 18 x + 5

Maximum (1, 13), Minimum (3, 5)

Solution steps

f^{'} (x) = 6 x^{2} - 24 x + 18

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 1

into

2 x^{3} - 12 x^{2} + 18 x + 5 : 13

Maximum (1, 13)

Plug

x = 3

into

2 x^{3} - 12 x^{2} + 18 x + 5 : 5

Minimum (3, 5)

Maximum (1, 13), Minimum (3, 5)

f (x) = 2 x \cdot ln (x)

f (x) = 5 x^{\frac{1}{3}} - x^{\frac{5}{3}}

6 x^{2} + 30 x - 84

y = r - (x - r)^{2}

f (x) = 2 x^{3} - 30 x^{2} + 96 x + 4, 0 \leq x \leq 12

What is the extreme f(x)=2x^3-12x^2+18x+5 ?
The extreme f(x)=2x^3-12x^2+18x+5 is Maximum(1,13),Minimum(3,5)