What is the extreme f(x)=x^{5/4}-80x^{1/4} ?

The extreme f(x)=x^{5/4}-80x^{1/4} is Maximum(0,0),Minimum(16,-128)

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extreme f(x)=x^{5/4}-80x^{1/4}

extreme points

f (x) = x^{\frac{5}{4}} - 80 x^{\frac{1}{4}}

Maximum (0, 0), Minimum (16, - 128)

Solution steps

f^{'} (x) = \frac{5 x - 80}{4 x ^{\frac{3}{4}}}

Find intervals:

Decreasing

: 0 < x < 16,

Increasing

: 16 < x < \infty

Plug

x = 0

into

x^{\frac{5}{4}} - 80 x^{\frac{1}{4}} : 0

Maximum (0, 0)

Plug

x = 16

into

x^{\frac{5}{4}} - 80 x^{\frac{1}{4}} : - 128

Minimum (16, - 128)

Maximum (0, 0), Minimum (16, - 128)

f (x) = 5 + 6 x - x^{2}, 0 \leq x \leq 4

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

f (x) = - x^{3} + 8 x^{2} - 15 x

y = 2 x^{3} - 15 x^{2} + 24 x - 5

f (x) = - 7 x^{2} + 42 x + 5

What is the extreme f(x)=x^{5/4}-80x^{1/4} ?
The extreme f(x)=x^{5/4}-80x^{1/4} is Maximum(0,0),Minimum(16,-128)