What is the extreme f(x)=2x^3+6x^2-18x+7 ?

The extreme f(x)=2x^3+6x^2-18x+7 is Maximum(-3,61),Minimum(1,-3)

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extreme f(x)=2x^3+6x^2-18x+7

extreme points

f (x) = 2 x^{3} + 6 x^{2} - 18 x + 7

Maximum (- 3, 61), Minimum (1, - 3)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 3

into

2 x^{3} + 6 x^{2} - 18 x + 7 : 61

Maximum (- 3, 61)

Plug

x = 1

into

2 x^{3} + 6 x^{2} - 18 x + 7 : - 3

Minimum (1, - 3)

Maximum (- 3, 61), Minimum (1, - 3)

f (x) = 2 x^{3} + 6 x^{2} - 18 x + 6

f (x) = 2 x^{3} + 6 x^{2} - 18 x + 1

Q (a, b) = 7 a (a - 2 b) + a (a - 3 b) + 2 a^{2} - 8 b^{2}

g (y, z) = y^{2} z^{3} + π yz

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

What is the extreme f(x)=2x^3+6x^2-18x+7 ?
The extreme f(x)=2x^3+6x^2-18x+7 is Maximum(-3,61),Minimum(1,-3)