increasing decreasing and more
posted by Jen on .
How to analytically find the intervals on which the function y = 2x^4 - 4x^2 + 1 is
Also find any local extreme values and inflection points.
(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.