How do you find all points of inflection given #y=x^5-2x^3#?
1 Answer
Nov 10, 2016
There is just one point of inflection at the origin
Explanation:
# y = x^5 - 2x^3 #
Differentiating wrt
# dy/dx = 5x^4 - 6x^2 #
At a critical point ,
So, Either
So critical points occurs when
Next we can find the nature of th critical points by looking at the second derivative:
# dy/dx = 5x^4 - 6x^2 #
# :. (d^2y)/(dx^2) = 20x^3 - 12x #
# :. (d^2y)/(dx^2) = 4x(5x^2 - 3) #
When
So therei is one point of inflection when