Question

(a) Find the slope of the tangent line to the parabola $ y = 4x - x^2 $ at the point $ (1, 3) $ (i) using Definition 1 (ii) using Equation 2 (b) Find an equation of the tangent line in part (a). (c) Graph the parabola and the tangent line. As a check on your work, zoom in toward the point $ (1, 3) $ until the parabola and the tangent line are indistinguishable.

Name: Problem 3, Chapter 2: Calculus: Early Transcendentals
Uploaded: 2021-08-25T23:45:35-08:00
Duration: 2 min 51 s
Channel: David Mccaslin
Description: (a) Find the slope of the tangent line to the parabola y = 4x - x^2 at the point (1, 3) (i) using Definition 1 (ii) using Equation 2 (b) Find an equation of the tangent line in part (a). (c) Graph the parabola and the tangent line. As a check on your work, zoom in toward the point (1, 3) until the parabola and the tangent line are indistinguishable.

   (a) Find the slope of the tangent line to the parabola $ y = 4x - x^2 $ at the point $ (1, 3) $
(i) using Definition 1    (ii) using Equation 2

(b) Find an equation of the tangent line in part (a).

(c) Graph the parabola and the tangent line. As a check on your work, zoom in toward the point 
$ (1, 3) $ until the parabola and the tangent line are indistinguishable.

Calculus: Early Transcendentals

James Stewart 8th Edition

Chapter 2, Problem 3

Instant Answer

Solved by Expert David Mccaslin

08/25/2021

Step 1

The derivative of a function gives us the slope of the tangent line at any point on the curve. The derivative of $4x$ is $4$ and the derivative of $-x^2$ is $-2x$. So, the derivative of the function is $4 - 2x$. Show more…

Show all steps

Thanks for your feedback!

(a) Find the slope of the tangent line to the parabola $ y = 4x - x^2 $ at the point $ (1, 3) $ (i) using Definition 1 (ii) using Equation 2 (b) Find an equation of the tangent line in part (a). (c) Graph the parabola and the tangent line. As a check on your work, zoom in toward the point $ (1, 3) $ until the parabola and the tangent line are indistinguishable.