Question

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)

Answer 1

You will need the first derivative. Go!

Answer 2

Is it 2x

Answer 3

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

Answer 4

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 \(\large\rm m\).

Answer 5

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.

Answer 6

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

Answer 7

Yup, that makes sense

Answer 8

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.

Answer 9

Thanks so much!!