What is the extreme f(x)=x^4(x-5)+4 ?

The extreme f(x)=x^4(x-5)+4 is Maximum(0,4),Minimum(4,-252)

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extreme f(x)=x^4(x-5)+4

extreme points

f (x) = x^{4} (x - 5) + 4

Maximum (0, 4), Minimum (4, - 252)

Solution steps

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

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < 4,

Increasing

: 4 < x < \infty

Plug

x = 0

into

x^{4} (x - 5) + 4 : 4

Maximum (0, 4)

Plug

x = 4

into

x^{4} (x - 5) + 4 : - 252

Minimum (4, - 252)

Maximum (0, 4), Minimum (4, - 252)

f (x) = x^{2} - \frac{54}{x}

y = \frac{1}{9} [\frac{t ^{3}}{3} + \frac{3 t ^{2}}{2} - 28 t]

2 x^{3} + 3 x^{2} - 36 x + 3, - 3 \leq x \leq 6

x^{2} + 6 x + 3

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

What is the extreme f(x)=x^4(x-5)+4 ?
The extreme f(x)=x^4(x-5)+4 is Maximum(0,4),Minimum(4,-252)