What is the extreme y=-4x^3+60x^2-252x+8 ?

The extreme y=-4x^3+60x^2-252x+8 is Minimum(3,-316),Maximum(7,-188)

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extreme y=-4x^3+60x^2-252x+8

extreme points

y = - 4 x^{3} + 60 x^{2} - 252 x + 8

Minimum (3, - 316), Maximum (7, - 188)

Solution steps

f^{'} (x) = - 12 x^{2} + 120 x - 252

Find intervals:

Decreasing

: - \infty < x < 3,

Increasing

: 3 < x < 7,

Decreasing

: 7 < x < \infty

Plug

x = 3

into

- 4 x^{3} + 60 x^{2} - 252 x + 8 : - 316

Minimum (3, - 316)

Plug

x = 7

into

- 4 x^{3} + 60 x^{2} - 252 x + 8 : - 188

Maximum (7, - 188)

Minimum (3, - 316), Maximum (7, - 188)

f (x, y) = 10 - x^{2} y + 3 x y + x y^{2}

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

y = \frac{2 x}{x - 6}

f (t) = (e^{t} + 2 t - 1) u (t - 1)

f (x) = (x - 1) (x + 3)

What is the extreme y=-4x^3+60x^2-252x+8 ?
The extreme y=-4x^3+60x^2-252x+8 is Minimum(3,-316),Maximum(7,-188)