Chapter 13, Problem 32RE

To determine

To find an equation of the line tangent to the graph of $f$ at the given point

Answer to Problem 32RE

The equation is $4x-y=7$

Explanation of Solution

Given information:

Consider the given information,

  $f\left(x\right)=x^2\text{-3 at }\left(2,1\right)$

CALCULATION:

To find the equation is,

  $\begin{array}{l}f\left(x\right)=2^2-3\\ f\text{'}\left(x\right)=2x\\ \text{At}\left(2,1\right)\\ f\left(2\right)=2\times 2=4\\ \text{Therefore,}m=4\\ \text{Equation,}\left(y-y_1\right)=m\left(x-x_1\right)\\ =\left(y-6\right)=2\left(x-3\right)\\ =y-6=2x-6\\ =2x-y=0\end{array}$

Therefore, the equation of the line tangent to the graph of $f$ at the given point is $4x-y=7$