What is the extreme f(x)=2x^3-9x^2+12x+7 ?

The extreme f(x)=2x^3-9x^2+12x+7 is Maximum(1,12),Minimum(2,11)

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extreme f(x)=2x^3-9x^2+12x+7

extreme points

f (x) = 2 x^{3} - 9 x^{2} + 12 x + 7

Maximum (1, 12), Minimum (2, 11)

Solution steps

f^{'} (x) = 6 x^{2} - 18 x + 12

Find intervals:

Increasing

: - \infty < x < 1,

Decreasing

: 1 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = 1

into

2 x^{3} - 9 x^{2} + 12 x + 7 : 12

Maximum (1, 12)

Plug

x = 2

into

2 x^{3} - 9 x^{2} + 12 x + 7 : 11

Minimum (2, 11)

Maximum (1, 12), Minimum (2, 11)

f (x) = 2 x^{3} - 9 x^{2} + 12 x + 1

f (x, y) = x y - x^{2} - y^{2} + x + y + 17

f (x) = 50 y^{2} + x^{2} - x^{2} y

f (x) = 8 x^{\frac{3}{4}} - x, 0 \leq x \leq 4096

\frac{x ^{2} - 7}{x + 4}

What is the extreme f(x)=2x^3-9x^2+12x+7 ?
The extreme f(x)=2x^3-9x^2+12x+7 is Maximum(1,12),Minimum(2,11)