increasing decreasing and more
posted by Jen .
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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