Posted by **Jen** on Saturday, November 11, 2006 at 9:50pm.

How to analytically find the intervals on which the function y = 2x^4 - 4x^2 + 1 is

1)increasing

2)decreasing

3)concave up

4)concave down

Also find any local extreme values and inflection points.

Thanks.

(1) The function is increasing when the first derivative dy/dx = 8x^3 - 8x is positive

(2) The function is decreasing there the same derivative is negative.

(3) The function is concave up where the second derivative, 24 x^2 - 8, is positive.

(4) The function is concave down where the second derivative is negative.

Extreme values occur whereever dy/dx = 0

Inflection points are where the second deritivative is zero.

The rest is algebra.

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