What are the points of inflection of #f(x)=3x^5 - 5x^3 ##?
1 Answer
They are
Explanation:
Possible point of inflection is determine by setting the derivative equal to zero. Possible point on inflection happen when there is changes in concavity (refer to the graph below)
#f'(x) = 15x^4 -15x^2#
#f''(x) = 60x^3 -30x#
Set the second derivative equal to zero
#30x(2x^2 -1) = 0#
#x^2-1 = 0=> 2x^2= 1#
#x^2 =1/2>x = +-sqrt(1/2) => +- sqrt(2)/2#
Coordinates point for P.O.I (Point of inflection)
#(3)(-sqrt2/8) -5(-sqrt2/8)=-3sqrt2/8+5sqrt2/8 #
#2sqrt2/8=>sqrt2/4==> (-sqrt2/2,sqrt2/4)#
#(3)(sqrt2/8) -5(sqrt2/8)=3sqrt2/8-5sqrt2/8 #
#-2sqrt2/8=>-sqrt2==> (-sqrt2/2,-sqrt2/4)#
graph{3x^5-5x^3 [-10, 10, -5, 5]}