The Slope of the Curve, Derivatives

[MorganJ]

1. Find the derivative f' of f(x)=x^2. Then find the slope of the curve y=f(x) at x=3 and write an equation for the tangent line.


2. I know that the derivative of x^2 is 2x and I'm guessing that y=x^2, therfore, (3)^2 = 9 which is the value of y. So now the point is (3,9). How do I find the slope? Do I do rise over run which is 9/3 which is 3?

3. I already know the tangent line equation but the slope is getting me confused. I know slope is y=mx+b But what if this is with derivatives?

 

[nicksauce]

3. I already know the tangent line equation but the slope is getting me confused. I know slope is y=mx+b But what if this is with derivatives?

No. The equation of the line is y = mx + b. m is the slope and b is the y intercept.

To find the slope of the tangent line, note that the derivative of a function at a point gives the slope of the tangent line. Then you have one point (3,9) and the slope, so you should be able to find the equation of the line.

 

[Дьявол]

The equation of the tangent line is:

y-y_0=f'(x_0)(x-x_0)

In this case x₀=3 and y₀=9

Regards.