Finding the Slope of Secant and Tangent Lines

[cvc121]

Homework Statement

The points P (2,-1) and Q (3,-4) lie on the parabola y = -x²+2x-1
a) Find the slope of the secant line PQ.
b) Find the slope of the tangent line to the parabola to the parabola at P.
c) Find the equation of the tangent line at P.

Homework Equations

The Attempt at a Solution

I am just new to calculus and am having trouble determining the slope of a secant and tangent line. My attempt at the questions are attached. Can anyone verify my work to see if I am on the right track? Are my methods for solving for the slopes correct? Thanks! All help is very much appreciated!

 

[brainpushups]

Yup. Looks good.

 

[SammyS]

Homework Statement

The points P (2,-1) and Q (3,-4) lie on the parabola y = -x²+2x-1
a) Find the slope of the secant line PQ.
b) Find the slope of the tangent line to the parabola to the parabola at P.
c) Find the equation of the tangent line at P.

Homework Equations

The Attempt at a Solution

I am just new to calculus and am having trouble determining the slope of a secant and tangent line. My attempt at the questions are attached. Can anyone verify my work to see if I am on the right track? Are my methods for solving for the slopes correct? Thanks! All help is very much appreciated!

It looks fine.