What is the extreme y=5x^7+2x^3+6 ?

The extreme y=5x^7+2x^3+6 is Saddle(0,6)

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extreme y=5x^7+2x^3+6

extreme points

y = 5 x^{7} + 2 x^{3} + 6

Saddle (0, 6)

Solution steps

Find the critical points:

x = 0

Domain of

5 x^{7} + 2 x^{3} + 6 : - \infty < x < \infty

Find intervals:

Increasing

: - \infty < x < 0,

Increasing

: 0 < x < \infty

Plug the extreme point

x = 0

into

5 x^{7} + 2 x^{3} + 6 \Rightarrow y = 6

Saddle (0, 6)

f (x) = \frac{1}{2} x^{2} + 6 x + 5

y = \frac{1}{2} x^{2}

y = x^{2} - x^{4}

sin (2 x + 1)

f (x) = (2 x) - \frac{3}{5}