(a) Find the slope m of the tangent to the curve y = 8 + 5x² - 2x³ at the point where x = a. m= (b) Find equations of the tangent lines at the points (1, 11) and (2, 12). y(x)= (at the point (1, 11)) y(x) = (c) Graph the curve and both tangents on a common screen. y -10 -10 (at the point (2, 12)) -5 -5 15- 10 10 20 15 10 10F 10 5 15 10 X X -10. -10 45 y -5 15 10 5 -10F 20 15 10 -5 -10 5 10 5 15 10 X X

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Question

Use limit definition to of derivative to find f'.

(a) Find the slope m of the tangent to the curve y = 8 + 5x² - 2x³ at the point where x = a.
(b) Find equations of the tangent lines at the points (1, 11) and (2, 12).
y(x) =
(at the point (1, 11))
Y(x)=
(c) Graph the curve and both tangents on a common screen.
y
0
-10
-10
(at the point (2, 12))
-5
-5
15
10
-5
y
-10
20
15
10
5
10
5
15
10
X
0
-10
5
10
- 10h
y
20
5
-5
-10
5
10
15
10
X
Transcribed Image Text:(a) Find the slope m of the tangent to the curve y = 8 + 5x² - 2x³ at the point where x = a. (b) Find equations of the tangent lines at the points (1, 11) and (2, 12). y(x) = (at the point (1, 11)) Y(x)= (c) Graph the curve and both tangents on a common screen. y 0 -10 -10 (at the point (2, 12)) -5 -5 15 10 -5 y -10 20 15 10 5 10 5 15 10 X 0 -10 5 10 - 10h y 20 5 -5 -10 5 10 15 10 X
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