Answer :
The only points that coincide are at x = 0,only 1 of the inflection points is also an extremum.
What is inflection points ?
An inflection point, point of inflection, flex, or inflection is a point on a smooth plane curve where the curvature changes sign in differential calculus and differential geometry.
First find the extrema (zeros of the derivative).
f (x) = 12x^5 - 5x^4
f '(x) = 60x^4 -20x^3
= 20x^3(3x - 1)
x = 0 x =1/3
So the extrema occur at x = 0 and x =1/3.
Now find the inflection points (zeros of the 2ndderivative).
f '(x) = 60x^4 -20x3^
f ''(x) = 240x^3 -60x^2
= 60x^2(4x - 1)
x = 0 x =1/4
The inflection points occur at x = 0 and x =1/4.
Since the only points that coincide are at x = 0,only 1 of the inflection points is also an extremum.
To learn more about inflection point visit:https://brainly.com/question/29017999
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The only points that coincide are at x = 0,only 1 of the inflection points is also an extremum.
What is inflection points ?
An inflection point, point of inflection, flex, or inflection is a point on a smooth plane curve where the curvature changes sign in differential calculus and differential geometry.
First find the extrema (zeros of the derivative).
f (x) = 12x^5 - 5x^4
f '(x) = 60x^4 -20x^3
= 20x^3(3x - 1)
x = 0 x =1/3
So the extrema occur at x = 0 and x =1/3.
Now find the inflection points (zeros of the 2ndderivative).
f '(x) = 60x^4 -20x3^
f ''(x) = 240x^3 -60x^2
= 60x^2(4x - 1)
x = 0 x =1/4
The inflection points occur at x = 0 and x =1/4.
Since the only points that coincide are at x = 0,only 1 of the inflection points is also an extremum.
To learn more about inflection point visit:brainly.com/question/29017999
#SPJ1
