Tangent Line Calculator

The calculator will find the tangent line to the explicit, polar, parametric and implicit curve at the given point, with steps shown.

It can handle horizontal and vertical tangent lines as well.

Choose type:

Enter a function:
Enter a point:
`x_0=`( )

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Solution

Your input: find the tangent line to $$$f\left(x\right)=x^{2}$$$ at $$$x_0=1$$$

We are given that $$$x_0=1$$$

Firstly, find the value of the function at the given point: $$$y_0=f\left(1\right)=1$$$

Secondly, find the slope of the tangent line, which is the derivative of the function, evaluated at the point: $$$m=f^{\prime}\left(1\right)$$$

Find the derivative: $$$f^{\prime}\left(x\right)=2 x$$$ (steps can be seen here).

Next, evaluate the derivative at the given point to find the slope.

$$$m=f^{\prime}\left(1\right)=2$$$

Finally, the equation of the tangent line is $$$y-y_0=m(x-x_0)$$$

Plugging the found values, we get that $$$y-\left(1\right)=2\left(x-\left(1\right)\right)$$$

Or, more simply: $$$y=2 x-1$$$

Answer: $$$y=2 x-1 $$$