What is the extreme f(x)=8x^{3/4}-x ?

The extreme f(x)=8x^{3/4}-x is Maximum(0,0),Maximum(1296,432)

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extreme f(x)=8x^{3/4}-x

extreme points

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

Maximum (0, 0), Maximum (1296, 432)

Solution steps

f^{'} (x) = \frac{6}{x ^{\frac{1}{4}}} - 1

Find intervals:

Decreasing

: 0 \leq x < \frac{1}{1296},

Increasing

: \frac{1}{1296} < x < \infty

Plug

x = 0

into

8 x^{\frac{3}{4}} - x : 0

Maximum (0, 0)

Plug

x = 1296

into

8 x^{\frac{3}{4}} - x : 432

Maximum (1296, 432)

Maximum (0, 0), Maximum (1296, 432)

f (x) = - 5 x^{6} ln (x)

E (a, b) = (2 a + b)^{2} - (a + b) (a - b)

f (x, y) = x^{2} - y^{2} + 1

y = x^{4} - 3 x^{2} = x^{2} (x^{2} - 3)

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

What is the extreme f(x)=8x^{3/4}-x ?
The extreme f(x)=8x^{3/4}-x is Maximum(0,0),Maximum(1296,432)