What is the extreme f(x)=5x^5-3x^2+x-10 ?

The extreme f(x)=5x^5-3x^2+x-10 is Maximum(0.17015…,-9.91599…),Minimum(0.55115…,-10.10586…)

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extreme f(x)=5x^5-3x^2+x-10

extreme points

f (x) = 5 x^{5} - 3 x^{2} + x - 10

Maximum (0.17015 \dots, - 9.91599 \dots), Minimum (0.55115 \dots, - 10.10586 \dots)

Solution steps

Find the critical points:

x \approx 0.17015 \dots, x \approx 0.55115 \dots

Domain of

5 x^{5} - 3 x^{2} + x - 10 : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < 0.17015 \dots,

Decreasing

: 0.17015 \dots < x < 0.55115 \dots,

Increasing

: 0.55115 \dots < x < \infty

Plug the extreme point

x = 0.17015 \dots

into

5 x^{5} - 3 x^{2} + x - 10 \Rightarrow y = - 9.91599 \dots

Maximum (0.17015 \dots, - 9.91599 \dots)

Plug the extreme point

x = 0.55115 \dots

into

5 x^{5} - 3 x^{2} + x - 10 \Rightarrow y = - 10.10586 \dots

Minimum (0.55115 \dots, - 10.10586 \dots)

Maximum (0.17015 \dots, - 9.91599 \dots), Minimum (0.55115 \dots, - 10.10586 \dots)

f (x) = ln (x^{2} + x + 1), - 1 \leq x \leq 1

f (x) = x^{2} + x y + y^{2} - 28 y + 261

\frac{- x + 3}{x ^{2} + 14 x + 49}

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

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

What is the extreme f(x)=5x^5-3x^2+x-10 ?
The extreme f(x)=5x^5-3x^2+x-10 is Maximum(0.17015…,-9.91599…),Minimum(0.55115…,-10.10586…)