Suppose that f (0) = 2 and f'(x) < 3 for all x > 0.Show that f(4) < 14 by considering f on the interval I = [0,4].Show that f(x) < 2 + 3.x for any x > 0.

f(0)=2 and f'(x)≤3 for all x>0 ⋯(i)integrate (i) w.r.to x ,we getf(x)≤3x+kput…

Answered: Suppose that f (0) = 2 and f'(x) < 3…

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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Suppose that f (0) = 2 and f'(x) < 3 for all x > 0.
Show that f(4) < 14 by considering f on the interval I = [0,4].
Show that f(x) < 2 + 3.x for any x > 0.

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$f (0) = 2 a n d f' (x) \leq 3 f o r a l l x > 0 \dots (i) i n t e g r a t e (i) w . r . t o x, w e g e t f (x) \leq 3 x + k p u t x = 0 f (0) \leq 3 \times 0 + k = k 2 \leq k \Rightarrow f (x) \leq 3 x + 2 f o r a l l x > 0 n o w p u t x = 4 f (4) \leq 3 \times 4 + 2 = 14$

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