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11 Nov 2022

6 min read

**Critical Point Calculator**. The critical points are crucial in finding the range of particular algebraic functions and finding the roots, where the derivation is impossible. The critical points don't exist if the slope is not changing from the negative to positive and vice versa.

The **critical point** is a term widely **used in Mathematics**, and it is a point where a function is not differentiable. There is a domain and range of every **algebraic function** but at the critical point, it is impossible to differentiate a function. A **critical point calculator** makes it easy to find the critical point of any algebraic function. You can understand the term critical point simply as the point where you would not able to find the gradient.

It means the gradient or the slope is undefined at this point. The critical point of the **multidimensional function** is the point where the derivative is equal to zero. This means you would not able to find the derivative of the function at the critical point. The online critical point finder can compute the critical point of a single and multidimensional function. Just use the **critical point calculator** to find the derivative of a multidimensional algebraic function in steps.

In the following article, we are discussing how you can find the critical point in the steps:

Now we solve an example to explain how we can find the **critical point in steps**. This would explain the methodology of how to find the critical point.

Consider a function 4x2+ 8xy+ 2y, we would find the critical point of the multidimensional functions 4x2+ 8xy+ 2y. You need to recognize there are two functions x and y involved in the function 4x2+ 8xy+ 2y. The critical points calculator automatically recognizes whether the function is a multifunction or a single variable function. The critical points are essential to finding the range of an algebraic function.

We are doing the steps of derivation computation of the **function to find the critical point**:

We need to find the derivative with respect to “x” and “y” of the function 4x2+ 8xy+ 2y. If you are finding any difficulty to compute just use the online critical number calculator.

Derivative with respect to “x”

Now the derivative with respect to “x” is:

F(x)=4x2+ 8xy+ 2y

Now apply the power rules and the x goes to the “1”

/x = 8x+ 8(1) y+0

/x = 8x+8y+0

/x = 8x+8y

Compute the derivative with respect to “x” by the 4x2+ 8xy+ 2y critical numbers calculator.

Derivative with respect to “y”

Now the derivative with respect to “y” is:

F(y)=4x2+ 8xy+ 2y

Now apply the power rules and the y goes to the “1”

/y = 0+ 8x(1)+ 2(1)

/y = 8x(1)+ 2(1)

/y = 8x+ 2

The critical point calculator can be used to find the derivative with respect to the “y”.

For finding the critical point, we need to enter the values of derivative f'(x,y) = 0 to zero.

Now:

/x =0

8x+8y=0-----------(1)

/y =0

8x+ 2=0-----------(2)

For finding the critical value, we are comparing the derivative with respect to the “x” and “y” with the zero.

Compute the values of “x” or “y” from one equation and substitute the values in the second equation:

Now consider the equation:

8x+ 2=0

Then

x = -2/8 or x=-1/4

x=-1/4

Insert the values of the x=-¼ in the equation (1), to find the value of “y”

8x+8y=0-----------(1)

8(-¼)+8y=0

Then

-2+8y=0

y=2/8=1/4

y =1/4

It is handy to use the critical point calculator to compute the derivative of a multidimensional algebraic function in steps.

Now when we enter the critical points (-1/4, ¼), the equation (1) and (2) will be uncomputable. These are the points where we can’t find the gradient or slope of the function 4x2+ 8xy+ 2y.

Conclusion:

The critical points are the point where the gradient or the derivative of an algebraic function is impossible to compute. The critical points are used to find the range of functions and the maximum and minimum values of an algebraic function.