Inflection Point Calculator

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Points of inflection play a pivotal role in functions and curves. Points of inflection are points on the curve which can change the curvature or concavity of the curve. The online tool used to calculate the points of inflection for a given function is called as points of inflection calculator.

Example 1: Find the inflection points of the function f(x) = x2 + 6x

Given is a function f(x) = x2 + 5x

The first derivative of the function needs to be calculated to find the points of inflection.

f'(x) = 3 x + 6

Now check for the points of inflection by having f'(x) = 0

3x + 6 =0 subtract 6 on both sides.

3x = -6 divide by 3 on both sides.

x = -2 and f (-2) = -22 + 6(-2) = 4 – 12 = -8

Hence the points of inflection = (-2, -8)

Example 2: Find the inflection points of the function f(x) = x3 - 75x

Given is a function f(x) = x3 - 75x

The first derivative of the function needs to be calculated

f'(x) = 3x2 - 75

Now check for the points of inflection by having f'(x) = 0

3x2 - 75 =0  add 75 on both sides.

3x2 = 75  divide by 3 on both sides.

x 2 = 25  x = 5 and -5  f(5) = -250 and f(-5) = 250

Hence the points of inflection are (5, -250) and (-5, 250).