Question

Use the definition of the derivative to find the equations of the lines described in Exercises 59-64.

The tangent line to $f\left(x\right)=x^2$ at$x=0$

Short answer

The equation of tangent is$y=2x^2$

Step-by-step solution

Step 1.Given information

Given the function$f\left(x\right)=x^2$and the point$x=0$

Use the formula for equation and calculate

Calculating, we get

$$\begin{gathered} y=f\left(c\right)+f^{\text{'}}\left(c\right)(x-c) \\ y=0+2x(x-0) \\ y=2x^2 \end{gathered}$$