I need help solving 7.3.1a) c) d) f) g) h) Hence explain, without using calculus, why ƒ is a monotonic function.eakly monotonic functicclass of functions which includes the strictly increareasing functions and functions whose graphs have some rising and sosections.horizonanumber of values of x, then f is strictly increasing.T < x2. A differentiable function f is non-increasing if and only if f'(x) <0 for allA non-increasing or non-decreasing function is said to be weakly monotonic.Exercises7.3.1 Which of the following functions are monotonic? Which are weakly monotonic?In each case, the domain of the function is R unless otherwise stated.(a) y = r³ + 3x(c) y = 5 – 26(e) y = 3/(1+x*)(8) y = x + |a|(b) y = 9x + x³ + 4x(d) y = 5 – a6 (x > 0)(f) y = (x+1)/(x – 1) (x > 1)(h) y%3D 2x + \미|7.3.2 In each of the following cases, find the range of values of the constant a for whichthe function f(x) is monotonic.(a) f(x) = (x+ a)³ – 80x (x E R);(b) f(x) = (x+a)% – 80x (x> 0);(c) f(x) = (x+ a)-2 + 80x (x > 0).7.3.3 As in panel (D) of Figure 7.1, let2xf(x)(-1 < x < 1).x2 - 1Show that, for all such r,1f(a)11+ x1- x

Answered: (a) y = r³ + 3x (c) y = 5 – 6 (b) y =…

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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I need help solving 7.3.1 a) c) d) f) g) h)

Hence explain, without using calculus, why ƒ is a monotonic function.
eakly monotonic functic
class of functions which includes the strictly increa
reasing functions and functions whose graphs have some rising and so
sections.
horizona
number of values of x, then f is strictly increasing.
T < x2. A differentiable function f is non-increasing if and only if f'(x) <0 for all
A non-increasing or non-decreasing function is said to be weakly monotonic.
Exercises
7.3.1 Which of the following functions are monotonic? Which are weakly monotonic?
In each case, the domain of the function is R unless otherwise stated.
(a) y = r³ + 3x
(c) y = 5 – 26
(e) y = 3/(1+x*)
(8) y = x + |a|
(b) y = 9x + x³ + 4x
(d) y = 5 – a6 (x > 0)
(f) y = (x+1)/(x – 1) (x > 1)
(h) y%3D 2x + \미|
7.3.2 In each of the following cases, find the range of values of the constant a for which
the function f(x) is monotonic.
(a) f(x) = (x+ a)³ – 80x (x E R);
(b) f(x) = (x+a)% – 80x (x> 0);
(c) f(x) = (x+ a)-2 + 80x (x > 0).
7.3.3 As in panel (D) of Figure 7.1, let
2x
f(x)
(-1 < x < 1).
x2 - 1
Show that, for all such r,
1
f(a)
1
1+ x
1- x

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a) Given function is $y = x^{3} + 3 x$

Draw graph of given function.

It is clearly visible from the graph with increase in value of 'x', value of 'y' increases as well. Therefore, given function is monotonic increasing over $ℝ$ .

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