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Popular >

extreme x^3-6x^2+1

Solution

extreme points

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

Solution

Maximum (0, 1), Minimum (4, - 31)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 0

into

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

Maximum (0, 1)

Plug

x = 4

into

x^{3} - 6 x^{2} + 1 : - 31

Minimum (4, - 31)

Maximum (0, 1), Minimum (4, - 31)

Popular Examples

extreme f(x)=2x^3+12x^2+18x extreme points

f (x) = 2 x^{3} + 12 x^{2} + 18 x

extreme f(x)= 4/3 x^3+7x^2-8x-42 extreme points

f (x) = \frac{4}{3} x^{3} + 7 x^{2} - 8 x - 42

extreme f(x)=2xsqrt(16-x^2)extreme points

f (x) = 2 x 16 - x^{2}

extreme f(x)=sqrt(16-x^2-y^2)extreme points

f (x) = 16 - x^{2} - y^{2}

extreme f(x,y)=25x^2+4y^2+4 extreme points

f (x, y) = 25 x^{2} + 4 y^{2} + 4

Frequently Asked Questions (FAQ)

What is the extreme x^3-6x^2+1 ?
The extreme x^3-6x^2+1 is Maximum(0,1),Minimum(4,-31)