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Popular >

extreme-x^3+6x^2

Solution

extreme points

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

Solution

Minimum (0, 0), Maximum (4, 32)

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

- x^{3} + 6 x^{2} : 0

Minimum (0, 0)

Plug

x = 4

into

- x^{3} + 6 x^{2} : 32

Maximum (4, 32)

Minimum (0, 0), Maximum (4, 32)

Popular Examples

extreme f(x)=6x^3-21x^2+36x-5 extreme points

f (x) = 6 x^{3} - 21 x^{2} + 36 x - 5

extreme f(x)= 1/3 x^3-2x^2-5x-10 extreme points

f (x) = \frac{1}{3} x^{3} - 2 x^{2} - 5 x - 10

extreme f(x)=3-x^{4/5}extreme points

f (x) = 3 - x^{\frac{4}{5}}

extreme f(x)=2xe^{-y}extreme points

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

extreme f(x)=8(1+1/x+1/(x^2))extreme points

f (x) = 8 (1 + \frac{1}{x} + \frac{1}{x ^{2}})

Frequently Asked Questions (FAQ)

What is the extreme-x^3+6x^2 ?
The extreme-x^3+6x^2 is Minimum(0,0),Maximum(4,32)