What is the extreme f(x)=x^5+3x^4-2x+1 ?

The extreme f(x)=x^5+3x^4-2x+1 is Maximum(-2.42794…,25.73482…),Minimum(0.51574…,0.21725…)

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extreme f(x)=x^5+3x^4-2x+1

extreme points

f (x) = x^{5} + 3 x^{4} - 2 x + 1

Maximum (- 2.42794 \dots, 25.73482 \dots), Minimum (0.51574 \dots, 0.21725 \dots)

Solution steps

Find the critical points:

x \approx - 2.42794 \dots, x \approx 0.51574 \dots

Domain of

x^{5} + 3 x^{4} - 2 x + 1 : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < - 2.42794 \dots,

Decreasing

: - 2.42794 \dots < x < 0.51574 \dots,

Increasing

: 0.51574 \dots < x < \infty

Plug the extreme point

x = - 2.42794 \dots

into

x^{5} + 3 x^{4} - 2 x + 1 \Rightarrow y = 25.73482 \dots

Maximum (- 2.42794 \dots, 25.73482 \dots)

Plug the extreme point

x = 0.51574 \dots

into

x^{5} + 3 x^{4} - 2 x + 1 \Rightarrow y = 0.21725 \dots

Minimum (0.51574 \dots, 0.21725 \dots)

Maximum (- 2.42794 \dots, 25.73482 \dots), Minimum (0.51574 \dots, 0.21725 \dots)

f (x) = - 2 x^{3} + 39 x^{2} - 240, 4 \leq x \leq 9

f (x) = 3 x^{2} e^{- 2 x} + 1

f (x) = 8 \frac{x ^{2}}{( x - 6 )}, - 3 \leq x \leq 2

f (x) = - 0.05 x^{2} + 300 x + 2000

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

What is the extreme f(x)=x^5+3x^4-2x+1 ?
The extreme f(x)=x^5+3x^4-2x+1 is Maximum(-2.42794…,25.73482…),Minimum(0.51574…,0.21725…)