What is the extreme y=x^3+4x^2-3x+6 ?

The extreme y=x^3+4x^2-3x+6 is Maximum(-3,24),Minimum(1/3 , 148/27)

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extreme y=x^3+4x^2-3x+6

extreme points

y = x^{3} + 4 x^{2} - 3 x + 6

Maximum (- 3, 24), Minimum (\frac{1}{3}, \frac{148}{27})

Solution steps

f^{'} (x) = 3 x^{2} + 8 x - 3

Find intervals:

Increasing

: - \infty < x < - 3,

Decreasing

: - 3 < x < \frac{1}{3},

Increasing

: \frac{1}{3} < x < \infty

Plug

x = - 3

into

x^{3} + 4 x^{2} - 3 x + 6 : 24

Maximum (- 3, 24)

Plug

x = \frac{1}{3}

into

x^{3} + 4 x^{2} - 3 x + 6 : \frac{148}{27}

Minimum (\frac{1}{3}, \frac{148}{27})

Maximum (- 3, 24), Minimum (\frac{1}{3}, \frac{148}{27})

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

f (x) = x^{2} - x^{\frac{1}{3}}, 0 \leq x \leq 1

f (x) = 3 x^{2} - 54 ln (x)

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

f (x, y) = - x^{2} + y^{2} + 6 x y + 4 x - 4 y + 7

What is the extreme y=x^3+4x^2-3x+6 ?
The extreme y=x^3+4x^2-3x+6 is Maximum(-3,24),Minimum(1/3 , 148/27)