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Popular >

extreme x^4-4x^3+8

Solution

extreme points

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

Solution

Saddle (0, 8), Minimum (3, - 19)

Solution steps

f^{'} (x) = 4 x^{3} - 12 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < 3,

Increasing

: 3 < x < \infty

Plug

x = 0

into

x^{4} - 4 x^{3} + 8 : 8

Saddle (0, 8)

Plug

x = 3

into

x^{4} - 4 x^{3} + 8 : - 19

Minimum (3, - 19)

Saddle (0, 8), Minimum (3, - 19)

Popular Examples

intercepts of f(x)=(x+2)/(2x+6)intercepts

f (x) = \frac{x + 2}{2 x + 6}

inverse of f(x)=ln(3x)inverse

f (x) = ln (3 x)

critical f(x)= 1/x critical points

f (x) = \frac{1}{x}

range of (x^2-16)/(2x+8)range

\frac{x ^{2} - 16}{2 x + 8}

shift-6cos(8x-pi/2)shift

- 6 cos (8 x - \frac{π}{2})

Frequently Asked Questions (FAQ)

What is the extreme x^4-4x^3+8 ?
The extreme x^4-4x^3+8 is Saddle(0,8),Minimum(3,-19)