Inflection Point Calculator | Calculate Inflection Point

Make use of this free handy Inflection Point Calculator to find the inflection points of a function within less time. Just enter function in the input fields shown below and hit on the calculate button which is in blue colour next to the input field to get the output inflection points of the given function in no time.

Inflection Point Calculator: Want to calculate the inflection point of a function in a simple way? Then you must try out this user friendly tool provided. It is one of the easiest ways that you ever find to compute the inflection point of a function. This page is all about Finding Inflection Point of the given function using a simple method and the interactive tutorial explaining each step of the process.

Steps to Find Inflection Point

Follow the below provided step by step process to get the inflection point of the function easily.

  • Take any function f(x).
  • Compute the first derivative of function f(x) with respect to x i.e f'(x).
  • Perform the second derivative of f(x) i.e f”(x) and also solve the third derivative of the function.
  • f”'(x) should not be equal to zero.
  • Make f”(x) equal to zero and find the value of variable.
  • Substitute x value in the third derivative of function to know the minimum and maximum values.
  • Replace the x value in the given function to get the y coordinate value.
  • Then, inflection points will be (x value, obtained value from function).

Find a variety of Other free Maths Calculators that will save your time while doing complex calculations and get step-by-step solutions to all your problems in a matter of seconds.


Question: Find the inflection points for the function f(x) = -x4 + 6x2?


Given function is f(x) = -x4 + 6x2

f'(x) = -4x3 + 12x

f”(x) = -12x2 + 12

f”'(x) = -24x

f”(x) = 0

-12x2 + 12 = 0

12 = 12x2

Divide by 12 on both sides.

1 = x2

x = ± 1

x1 = 1, x2 = -1

Substitute x = ± 1 in f”'(x)

f”'(1) = -24(1) = -24 < 0, then it is left hand bit to right hand bi.

f”'(-1) = -24(-1) = 24 > 0, then it is left hand bit to right hand bit.

Replace x = ± in f(x)

f(1) = -1+6 = 5

f(-1) = -1 +6 = 5

Therefore, inflection points are P1(, 5), P2(-, 5)

FAQs on Inflection Point Calculator

1. How do you find inflection points on a calculator?

Provide your input function in the calculator and tap on the calculate button to get the inflection points for that function.

2. What does inflection point mean?

Inflection point is defined as the point on the curve at which the concavity of the function changes. It can be a stationary point but not local maxima or local minima.

3. Find the point of inflection for the function f(x) = x5 – 5x4?

Given that

f(x) = x5 – 5x4

f'(x) = 5x4 – 20x3

f”(x) = 20x3 – 60x2

f”'(x) = 60x2 – 120x

Neccessary inflection point condition is f”(x) = 0

20x3 – 60x2 = 0

20x2(x-3) = 0

x1 = 0, x2 = 3

Substitute x2 = 3 in the f(x)

f(3) = 35 – 5*34 = 243 – 405 = -162

Inflection Point is (3, -162).

4. What is the difference between inflection point and critical point?

A critical point is a point on the graph where the function’s rate of change is altered wither from increasing to decreasing or in some unpredictable fashion. Inflection point is a point on the function where the sign of second derivative changes (where concavity changes). A critical point becomes the inflection point if the function changes concavity at that point.