What is the extreme 2t^3-24t^2+70 ?

The extreme 2t^3-24t^2+70 is Maximum(0,70),Minimum(8,-442)

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extreme 2t^3-24t^2+70

extreme points

2 t^{3} - 24 t^{2} + 70

Maximum (0, 70), Minimum (8, - 442)

Solution steps

f^{'} (t) = 6 t^{2} - 48 t

Find intervals:

Increasing

: - \infty < t < 0,

Decreasing

: 0 < t < 8,

Increasing

: 8 < t < \infty

Plug

t = 0

into

2 t^{3} - 24 t^{2} + 70 : 70

Maximum (0, 70)

Plug

t = 8

into

2 t^{3} - 24 t^{2} + 70 : - 442

Minimum (8, - 442)

Maximum (0, 70), Minimum (8, - 442)

y = x^{2} e^{x} - 2

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

7 x - 0.005 x^{2} - 3.6 x - 70

+ x^{2} - 2 x - 8

f (x) = 7 x y - λ (6 x + 11 y - 2)

What is the extreme 2t^3-24t^2+70 ?
The extreme 2t^3-24t^2+70 is Maximum(0,70),Minimum(8,-442)