## Anthonyn2121 one year ago Find the slope of the curve at the given point P, and an equation of the tangent line at P y=x^2-3, P(2,1)

1. tkhunny

You will need the first derivative. Go!

2. Anthonyn2121

Is it 2x

3. zepdrix

$$\large\rm y'(x)=2x$$ good :)

4. zepdrix

A tangent line is just a straight line. So it'll have the form: $$\large\rm y=mx+b$$ in slope-intercept form and $$\large\rm y-y_1=m(x-x_1)$$ in point-slope form. The process of taking the derivative of the function is what gives us our $$\large\rm m$$.

5. zepdrix

So at the point P(2,1), our x coordinate is 2. So we want to know the slope of our function (the derivative value), at x=2.

6. zepdrix

$\large\rm y'(2)=2(2)=m$Ok with that part? :o

7. Anthonyn2121

Yup, that makes sense

8. zepdrix

To get your final answer it would probably make more sense, at least for this problem, to go with point-slope form of a line. $\large\rm y-y_1=m(x-x_1)$Plug in your $$\large\rm m$$, plug in your $$\large\rm P$$, and bam you're done.

9. Anthonyn2121

Thanks so much!!