Finding the maximum value of algebraic expression

Asked Aug 09 '19 at 09:44

Active Aug 09 '19 at 12:36

Viewed 125 times

What is the maximum value of

$(ax+b)^\frac12 + (cx+d)^\frac12$

I did it using the concept $AM>=GM$

$\frac{(ax+b)^\frac12+(cx+d)^\frac12}2 \geq ((ax+b)^\frac12(cx+d)^\frac12)^\frac12$

And on solving this I found that $x\leq(b-d)/(c-a)$

And when $x$ is maximum value of the expression will be maximum

But this was not the answer. Somebody help me, please.

edited Aug 09 '19 at 11:14

zoli

asked Aug 09 '19 at 09:44

Kshitij Singh

Did you try with algebra ? – Claude Leibovici Aug 09 '19 at 09:51
1

Do you mean the minimum value when $x \in \mathbb R$? Or is there some restriction on $a,b,c,d$? – Toby Mak Aug 09 '19 at 09:54
Consider the function $$f(x)=\sqrt{ax+b}+\sqrt{cx+d}$$ and differentiate with respect to $x$ – Dr. Sonnhard Graubner Aug 09 '19 at 09:57
Differentiation gives minima – Kshitij Singh Aug 09 '19 at 10:10
1

if $a,b>0$ then $ (ax+b)^\frac12 + (cx+d)^\frac12$ is not bounded and increasing so it does not make sense to look for a maximum value. – miracle173 Aug 09 '19 at 12:17

0 Answers0