A function y = f(x) and an x-value xo are given. f(x) = x + Vr; xo = 1 (a) Find a formula for the slope of the tangent line to the graph of f at a general point xp. (b) Use the formula obtained in part (a) to find the slope of the tangent line for the given value of xo. a1) (a) Find a formula for the slope of the tangent line to the graph of fat a general point xp. The slope of the tangent line to f(x) at. xo is given by Def 2.1.1: Suppose that xo is in the domain of the function f. The tangent line to the curve y = f(x) at the point P(xp, f(x)) is the line with f(x) – f(x) . equation y – f(x0) = man(x – xo) where muan = lim provided the limit exists. x- xo f(x) – f(x0). Rewriting man = lim using f(x) = x + Vĩ, we get х — Хо (x+ Vã) – xo + Vxo man lim- x - x0 (x + Vx) – (xo + V) Man = lim х — Хо

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
A function y = f(x) and an x-value xo are given.
f(x) = x + Vr; xo = 1
(a) Find a formula for the slope of the tangent line to the graph of f at a general point xp.
(b) Use the formula obtained in part (a) to find the slope of the tangent line for the given value of xo.
a1)
(a) Find a formula for the slope of the tangent line to the graph of fat a general point xp.
The slope of the tangent line to f(x) at. xo is given by Def 2.1.1:
Suppose that xo is in the domain of the function f. The tangent line to the curve y = f(x) at the point P(xp, f(x)) is the line with
f(x) – f(x) .
equation y – f(x0) = man(x – xo) where muan
= lim
provided the limit exists.
x- xo
f(x) – f(x0).
Rewriting man
= lim
using f(x) = x + Vĩ, we get
х — Хо
(x+ Vã) – xo + Vxo
man
lim-
x - x0
(x + Vx) – (xo + V)
Man = lim
х — Хо
Transcribed Image Text:A function y = f(x) and an x-value xo are given. f(x) = x + Vr; xo = 1 (a) Find a formula for the slope of the tangent line to the graph of f at a general point xp. (b) Use the formula obtained in part (a) to find the slope of the tangent line for the given value of xo. a1) (a) Find a formula for the slope of the tangent line to the graph of fat a general point xp. The slope of the tangent line to f(x) at. xo is given by Def 2.1.1: Suppose that xo is in the domain of the function f. The tangent line to the curve y = f(x) at the point P(xp, f(x)) is the line with f(x) – f(x) . equation y – f(x0) = man(x – xo) where muan = lim provided the limit exists. x- xo f(x) – f(x0). Rewriting man = lim using f(x) = x + Vĩ, we get х — Хо (x+ Vã) – xo + Vxo man lim- x - x0 (x + Vx) – (xo + V) Man = lim х — Хо
Find g'(3) given that f(3) = -5 and f'(3) = 4.
g(x) = 3x? – 5f(x)
g'(3) =
i
eTextbook and Media
2x + 1
g(x) =
f(x)
Round the answer to two decimal places.
g'(3) = i
eTextbook and Media
Transcribed Image Text:Find g'(3) given that f(3) = -5 and f'(3) = 4. g(x) = 3x? – 5f(x) g'(3) = i eTextbook and Media 2x + 1 g(x) = f(x) Round the answer to two decimal places. g'(3) = i eTextbook and Media
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