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Popular >

extreme x^4-5x^3

Solution

extreme points

x^{4} - 5 x^{3}

Solution

Saddle (0, 0), Minimum (\frac{15}{4}, - \frac{16875}{256})

Solution steps

f^{'} (x) = 4 x^{3} - 15 x^{2}

Find intervals:

Decreasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{15}{4},

Increasing

: \frac{15}{4} < x < \infty

Plug

x = 0

into

x^{4} - 5 x^{3} : 0

Saddle (0, 0)

Plug

x = \frac{15}{4}

into

x^{4} - 5 x^{3} : - \frac{16875}{256}

Minimum (\frac{15}{4}, - \frac{16875}{256})

Saddle (0, 0), Minimum (\frac{15}{4}, - \frac{16875}{256})

Popular Examples

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

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

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

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

extreme f(x)=2sin(x)extreme points

f (x) = 2 sin (x)

extreme f(x)=ln(x-y)+x^2+y extreme points

f (x) = ln (x - y) + x^{2} + y

extreme f(x,y)=x^3-y^3-2xy+6 extreme points

f (x, y) = x^{3} - y^{3} - 2 x y + 6

Frequently Asked Questions (FAQ)

What is the extreme x^4-5x^3 ?
The extreme x^4-5x^3 is Saddle(0,0),Minimum(15/4 ,-16875/256)