Consider the following piecewise function: f(x)= excoxx, x<0 0sx<4 a. Use the first principles definition of a derivative to determine f'(x) when 0 ≤ x < 4 b. Determine /"(3) c. Determine the equation of the tangent to f(x) when x=-1 d. Determine f'(x) when x > 4 e. Is f(x) continuous when x = 47 Use the formal definition of continuity to argue your answer.
Consider the following piecewise function: f(x)= excoxx, x<0 0sx<4 a. Use the first principles definition of a derivative to determine f'(x) when 0 ≤ x < 4 b. Determine /"(3) c. Determine the equation of the tangent to f(x) when x=-1 d. Determine f'(x) when x > 4 e. Is f(x) continuous when x = 47 Use the formal definition of continuity to argue your answer.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help me with this. Please check if I have answered question. C) of this question correclty. Check if my answer is correct and If I have shown the right steps
Would the answer be y= 1 - pi/2 (x + pi/2) or y = - pi/2 x + (1 - pi/4 ^2)
Image 1: the question
Image 2: My work
Transcribed Image Text:c) f(x) =
d
clx
7 Let u XCOS X
when x =
XCOSX
T
d (xcosx)
cix
=xd (cosx) + cos x
ix20
E-xsinx + cos x
6
Now f(x) = eu
-> Differentiate with respect to 'x'
f'(x)= a(e)
TI/2
= d (eu) du (using chain (rule)
du
dx
(using product Rule)
(x)
zel (cosx-xsinx)
=excosx
dx
C=C1
(cosx-xsinx)
f(-1/2) = cos(- 11/2)
-T1/2 (0)
f'(- 1²) = 1 [cos (-1/2) - (-1) sin(-1/2)
= 1 (0-1)
-1
Equation of the tangent at the point x = - 11/2
and f(-11/2) = 1 is given by
T
=> (g-1) == (x + ¹)
=> y = - 1² - 11/2² + 1
-x
I
(y-1) = f'(-1/2)(x+1)
Thus the equation of the
tangent at x = -7/2 15
y = 1-1/2 (x + 7¹/₂)
Transcribed Image Text:Consider the following piecewise function: f(x) =
XCOLE x<0
0≤x≤4
a. Use the first principles definition of a derivative to determine f'(x) when 0 < x < 4
b. Determine f"(3)
c. Determine the equation of the tangent to f(x) when x = - =
d. Determine f'(x) when x > 4
e. Is f(x) continuous when x = 4? Use the formal definition of continuity to argue your answer...
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