What is the extreme y=2x^3+3x^2-12x+5 ?

The extreme y=2x^3+3x^2-12x+5 is Maximum(-2,25),Minimum(1,-2)

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extreme y=2x^3+3x^2-12x+5

extreme points

y = 2 x^{3} + 3 x^{2} - 12 x + 5

Maximum (- 2, 25), Minimum (1, - 2)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < - 2,

Decreasing

: - 2 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 2

into

2 x^{3} + 3 x^{2} - 12 x + 5 : 25

Maximum (- 2, 25)

Plug

x = 1

into

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

Minimum (1, - 2)

Maximum (- 2, 25), Minimum (1, - 2)

f (x) = 4 x + 4 sin (x), 0 \leq x \leq 2 π

f (x, y) = x^{2} + 7 x y + y^{2}

f (x) = 2 x^{2} - 16 ln (x)

f (x, y) = x 1 + y^{3}

f (x) = \frac{1 + x}{1 + x ^{2}}

What is the extreme y=2x^3+3x^2-12x+5 ?
The extreme y=2x^3+3x^2-12x+5 is Maximum(-2,25),Minimum(1,-2)