Point of Inflection Calculator

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Point of inflectioncalculator is very useful tool to find where the concavity will change. This tool uses point of inflection rules and formulas.One need to substitute the values only and it helps in finding the result automatically. This can be understood and easily evaluated by the following given below examples:-

Example 1:-

For the given function f(x) = x³, find the inflection point(s).

Solution 1:- We will find the 1^st and 2^nd derivatives of the function f(x) = x³

1^st derivative will be f’(x)=3x²

2^nd derivative will be f’(x)=6x

Now to find the point of inflection we have to make x=-1 and x=1.

f”(x) = 6x;

f”(-1) =-6;

f”(1)=6

This shows that function is concave up at x = 1. This shows that concavity actually changes at x zero. So this
function has no inflection point.

Example 2:-

For the given function f(x) = x³, find the inflection point(s).

Solution 2:- We will find the 1^st and 2^nd derivatives of the function f(x) = x³ + 3x²

1^st derivative will be f’(x)=3x² + 6x = 3x(x+2)

f’(x) = 0 ; 3x(x+2)=0

Either 3x=0 or x+2=0. So x=0 or x=-2

If we plug in x = 0, we have inflection point (0,0). When We Plug in x = -2

F(-2) = (-2)³+ 3 (-2)² = -6 + 12 = 6. Therefore inflection point is (-2,6)

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Point of Inflection Calculator

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