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# Critical Point Calculator

Enter the function and press calculate button to find the critical points

## Critical points calculator with steps

Critical points calculator finds the values of single or multivariable functions. This critical number calculator determines those points on which the function is not differentiable.

## What is the critical point?

A critical point is the point of the function at which the differential of the function is **zero **or **undefined**. It can also be defined as a point on the graph of a function where the differentiation is zero or infinite.

Critical points can be calculated by putting the first derivative equal to zero.

**f'(x) = 0**

## How to calculate the critical point?

To learn how to calculate the critical points, follow the below examples.

**Example 1**

Calculate the critical point of **3x^2 + 4x + 9.**

**Solution **

**Step I: **First of all, find the first derivative of the given function.

d/dx [3x^2 + 4x + 9] = d/dx [3x^2] + d/dx [4x] + d/dx [9]

d/dx [3x^2 + 4x + 9] = 6x + 4 + 0

`d/dx [3x^2 + 4x + 9] = 6x + 4`

**Step II: **Now calculate the critical point by substituting the first **derivative **equal to zero.

d/dx [3x^2 + 4x + 9] = 0

6x + 4 = 0

6x = -4

`x = -4/6 = -2/3`

Hence, the critical point of the given function is **x = -2/3**

**Example 2:**

Calculate the critical point of **4x^2 + 6xy + 8y**.

**Solution **

**Step I: **First of all, calculate the first partial derivative of the function w.r.t “x”.

∂/∂x [4x^2 + 6xy + 8y] = ∂/∂x [4x^2] + ∂/∂x [6xy] + ∂/∂x [8y]

∂/∂x [4x^2 + 6xy + 8y] = 8x + 6y + 0

`∂/∂x [4x^2 + 6xy + 8y] = 8x + 6y`

**Step II: **Now calculate the first partial derivative of the function w.r.t “**y**”.

∂/∂y [4x^2 + 6xy + 8y] = ∂/∂y [4x^2] + ∂/∂y [6xy] + ∂/∂y [8y]

∂/∂y [4x^2 + 6xy + 8y] = 0 + 6x + 8

`∂/∂y [4x^2 + 6xy + 8y] = 6x + 8`

**Step III: **Put the result of the first partial derivatives equal to zero.

**For ∂/∂x [f(x, y)]**

8x + 6y = 0

6y = -8x

`y = -8x/6 … (i)`

**For ∂/∂y [f(x, y)]**

6x + 8 = 0

6x = -8

`x = -8/6 = -4/3`

put the value of “**x**” in (**i**)

y = -8(-4/3)/6

y = 32/18

`y = 16/9`

Hence the critical points of the given function are:

**x = -4/3**

**y = 16/9**