Consider the function (a) Compute the derivative of f(x) directly from the limit definition. f(x+h)-f(x) h f'(x) = lim h→0 1 h→0 h = lim = : lim h→0 . (((4(x+h)-5)/(-4(x+h)-2))-(4x-5)/(-4x-2)) f(x) = (simplify to cancel h) 4x - 5 -4x - 2 = (b) Find an equation for the line tangent to y = f(x) at (−2, −1³). y = x+ (c) Find an equation for the line normal (ie perpendicular) to y = f(x) at (2, ³0). y = 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...
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Consider the function
(a) Compute the derivative of f(x) directly from the limit definition.
f(x+h)-f(x)
h
f'(x) = lim
h→0
1
: lim (((4(x+h)-5)/(-4(x+h)-2)-(4x-5)/(-4x-2))
h→0 h
lim
h→0
=
f(x) =
(simplify to cancel h)
4x5
-4x2
(b) Find an equation for the line tangent to y = f (x) at (−2, −1³).
y =
x+
(c) Find an equation for the line normal (ie perpendicular) to y = f (x) at (2, ³0).
y =
x+
Transcribed Image Text:Consider the function (a) Compute the derivative of f(x) directly from the limit definition. f(x+h)-f(x) h f'(x) = lim h→0 1 : lim (((4(x+h)-5)/(-4(x+h)-2)-(4x-5)/(-4x-2)) h→0 h lim h→0 = f(x) = (simplify to cancel h) 4x5 -4x2 (b) Find an equation for the line tangent to y = f (x) at (−2, −1³). y = x+ (c) Find an equation for the line normal (ie perpendicular) to y = f (x) at (2, ³0). y = x+
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