Question

(a) Find the slope of the tangent to the curve $ y = 3 + 4x^2 - 2x^3 $ at the point where $ x = a $. (b) Find equations of the tangent lines at the points $ (1, 5) $ and $ (2, 3) $. (c) Graph the curve and both tangents on a common screen.

Name: a find the slope of the tangent to the curve y 3 4x2 2x3 at the point where x a b find equations of the tangent lines at the points 1 5 and 2 3 c graph the curve and both tangents on a common screen 2
Uploaded: 2022-01-08T02:20:53-08:00
Duration: 4 min 10 s
Channel: Suman Saurav Thakur
Description: a find the slope of the tangent to the curve y 3 4x2 2x3 at the point where x a b find equations of the tangent lines at the points 1 5 and 2 3 c graph the curve and both tangents on a common screen 2

          (a) Find the slope of the tangent to the curve $ y = 3 + 4x^2 - 2x^3 $ at the point where $ x = a $.

(b) Find equations of the tangent lines at the points $ (1, 5) $ and $ (2, 3) $.

(c) Graph the curve and both tangents on a common screen.

Added by Amber H.

Calculus: Early Transcendentals

James Stewart 8th Edition

Chapter 2

Instant Answer

Solved by Expert Suman Saurav Thakur

01/08/2022

Step 1

To find the slope of the tangent at a point $x = a$, we first need to find the derivative of the function $y = 3 + 4x^2 - 2x^3$. The derivative is given by: $y' = 8x - 6x^2$ Now, evaluate the derivative at $x = a$ to find the slope of the tangent at that Show more…

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(a) Find the slope of the tangent to the curve $ y = 3 + 4x^2 - 2x^3 $ at the point where $ x = a $. (b) Find equations of the tangent lines at the points $ (1, 5) $ and $ (2, 3) $. (c) Graph the curve and both tangents on a common screen.