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Popular >

extreme 1+6x^2-x^3

Solution

extreme points

1 + 6 x^{2} - x^{3}

Solution

Minimum (0, 1), Maximum (4, 33)

Solution steps

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

Find intervals:

Decreasing

: - \infty < x < 0,

Increasing

: 0 < x < 4,

Decreasing

: 4 < x < \infty

Plug

x = 0

into

1 + 6 x^{2} - x^{3} : 1

Minimum (0, 1)

Plug

x = 4

into

1 + 6 x^{2} - x^{3} : 33

Maximum (4, 33)

Minimum (0, 1), Maximum (4, 33)

Popular Examples

extreme f(x)=x-3/2 x^{2/3}extreme points

f (x) = x - \frac{3}{2} x^{\frac{2}{3}}

extreme f(x)=x^4-8x^3+5 extreme points

f (x) = x^{4} - 8 x^{3} + 5

extreme f(x)=x^3-4x^2-3x+2 extreme points

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

extreme f(x)=4sqrt(x)-8x extreme points

f (x) = 4 x - 8 x

extreme f(x)=(x^2-x)^{1/3}extreme points

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

Frequently Asked Questions (FAQ)

What is the extreme 1+6x^2-x^3 ?
The extreme 1+6x^2-x^3 is Minimum(0,1),Maximum(4,33)