Find an equation of the tangent line to the graph of

Question

Find an equation of the tangent line to the graph of $F(x)=x^2$ at

1. $(3, 9)$

2. $(-1, 1)$

3. $(10, 100)$

Answer 1

If I do the first one you can apply it to the other two.

The slope of the tangent line is the derivative of $x^2 = 2x$

At point $(3, 9)$ the slope is $6$

The equation of the line going through $(3, 9$) with slope $6$ is:

$y = 6x + b$ where $b$ is the y intercept

$9 = 6(3) + b$

$b = 9 - 18 = -9$

Equation is: $y = 6x - 9$