What is the extreme 7x^4-4x^2-8x-5 ?

The extreme 7x^4-4x^2-8x-5 is Minimum(0.80139…,-11.09284…)

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extreme 7x^4-4x^2-8x-5

extreme points

7 x^{4} - 4 x^{2} - 8 x - 5

Minimum (0.80139 \dots, - 11.09284 \dots)

Solution steps

Find the critical points:

x \approx 0.80139 \dots

Domain of

7 x^{4} - 4 x^{2} - 8 x - 5 : - \infty < x < \infty

Find intervals:

Decreasing

: - \infty < x < 0.80139 \dots,

Increasing

: 0.80139 \dots < x < \infty

Plug the extreme point

x = 0.80139 \dots

into

7 x^{4} - 4 x^{2} - 8 x - 5 \Rightarrow y = - 11.09284 \dots

Minimum (0.80139 \dots, - 11.09284 \dots)

1 - (y + 1) 1 - y^{2} + y

f (x, y) = e^{x} - e^{x y}

f (x, y) = 2 x^{2} - 8 x y + 10 y^{2} + 10 x - 4 y - 5

3 + sin (x)

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

What is the extreme 7x^4-4x^2-8x-5 ?
The extreme 7x^4-4x^2-8x-5 is Minimum(0.80139…,-11.09284…)