Find the critical points and the intervals on which the function f(x)= 8x^5-2x^3

Question

Find the critical points and the intervals on which the function f(x)= 8x^5-2x^3+8 is increasing or decreasing. Use the First Derivative Test to determine whether the critical point is a local minimum or maximum. I found the critical point with local minimum to be: sqrt(3/5)/2 I found the critical point with local maximum to be: -sqrt(3/5)/2 Now I need to know the points of inflection, and on what intervals the function is increasing and decreasing on? Thanks!!!

Explanation / Answer

f(x)= 8x^5-2x^3+8 at critical point f'(x) = 0 => 40x^4 - 6x^2 = 0 =>x^2(40x^2 - 6) = 0 => x =0, sqrt(3/20) , -sqrt(3/20) for increasing value, f'(x)>0 =>x^2(40x^2 - 6) > 0 =>x>sqrt(3/20) , x

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