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Popular >

extreme x^4-4x^3+16x

Solution

extreme points

x^{4} - 4 x^{3} + 16 x

Solution

Minimum (- 1, - 11), Saddle (2, 16)

Solution steps

f^{'} (x) = 4 x^{3} - 12 x^{2} + 16

Find intervals:

Decreasing

: - \infty < x < - 1,

Increasing

: - 1 < x < 2,

Increasing

: 2 < x < \infty

Plug

x = - 1

into

x^{4} - 4 x^{3} + 16 x : - 11

Minimum (- 1, - 11)

Plug

x = 2

into

x^{4} - 4 x^{3} + 16 x : 16

Saddle (2, 16)

Minimum (- 1, - 11), Saddle (2, 16)

Popular Examples

extreme f(x)=15x^4-4x^3,-2<= x<= 2 extreme points

f (x) = 15 x^{4} - 4 x^{3}, - 2 \leq x \leq 2

extreme f(x)=x-1/2*y^2-1/3 x^3+y+6 extreme points

f (x) = x - \frac{1}{2} \cdot y^{2} - \frac{1}{3} x^{3} + y + 6

extreme f(x)=x^4-8x^3+18x^2 extreme points

f (x) = x^{4} - 8 x^{3} + 18 x^{2}

extreme f(x)=4x^3-3x^2-6x+3,(-1,10)extreme points

f (x) = 4 x^{3} - 3 x^{2} - 6 x + 3, (- 1, 10)

extreme y=2x^3-24x^2+90x+8 extreme points

y = 2 x^{3} - 24 x^{2} + 90 x + 8

Frequently Asked Questions (FAQ)

What is the extreme x^4-4x^3+16x ?
The extreme x^4-4x^3+16x is Minimum(-1,-11),Saddle(2,16)