What is the extreme x^4+8x^3-14x^2 ?

The extreme x^4+8x^3-14x^2 is Minimum(-7,-1029),Maximum(0,0),Minimum(1,-5)

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extreme x^4+8x^3-14x^2

extreme points

x^{4} + 8 x^{3} - 14 x^{2}

Minimum (- 7, - 1029), Maximum (0, 0), Minimum (1, - 5)

Solution steps

f^{'} (x) = 4 x^{3} + 24 x^{2} - 28 x

Find intervals:

Decreasing

: - \infty < x < - 7,

Increasing

: - 7 < x < 0,

Decreasing

: 0 < x < 1,

Increasing

: 1 < x < \infty

Plug

x = - 7

into

x^{4} + 8 x^{3} - 14 x^{2} : - 1029

Minimum (- 7, - 1029)

Plug

x = 0

into

x^{4} + 8 x^{3} - 14 x^{2} : 0

Maximum (0, 0)

Plug

x = 1

into

x^{4} + 8 x^{3} - 14 x^{2} : - 5

Minimum (1, - 5)

Minimum (- 7, - 1029), Maximum (0, 0), Minimum (1, - 5)

f (x) = 5 x^{2} - 30 x, 0 \leq x \leq 5

x \cdot e^{- x^{2}}

\frac{2 x + 4}{x ^{2} + 4}

f (x, y) = (5 x^{2} + 7 y^{2}) e^{- y}

8 - 4 x

What is the extreme x^4+8x^3-14x^2 ?
The extreme x^4+8x^3-14x^2 is Minimum(-7,-1029),Maximum(0,0),Minimum(1,-5)