1rationalize the denominator .. then differentiate .. this is going to be easy ...
if x ε R
find maximum value of 2(a-x)(x+√x2+b2)
any method other than dy/dx ?[7][7]
-
UP 0 DOWN 0 0 8
8 Answers
1
1its really turning out to be long that way...
no its not impossible
but anyone with a strikingly good idea ??
1f(x) = 2(a-x)(x-√x2+b2)/-b2
wat gud will this do [12] .. thinking ...........
66Let y=2(a-x)(\sqrt{x^2+b^2}+x)=\dfrac{2b^2(a-x)}{\sqrt{x^2+b^2}-x}
Cross multiply to get y\sqrt{x^2+b^2}=2b^2(a-x)+xy
Now square both sides and treat the resulting expression as a quadratic in x. Since the roots has to be real, make the discriminant positive and you finally obtain
y^2\big((a^2+b^2)-y\big)\geq 0
from where you obtain
y\leq (a^2+b^2)