IIT JEE 1983 Maths - MCQ Question 3

Calculus Level 3

If $f(x)=a\ln|x|+bx^2+x$ has its extremum values at $x=-1$ and $x=2$ , then which option is correct?

In case you are preparing for IIT JEE, you may want to try IIT JEE 1983 Mathematics Archives .

a=2, b=-1/2

None of the others

a=-2, b=1/2

a=2, b=-1

1 solution

Sabhrant Sachan
Dec 28, 2016

$\begin{aligned} f(x) & = a\log{|x|}+bx^2 +x \\ f^{'}(x) & = \dfrac{a}{|x|} \times \dfrac{x}{|x|} +2bx+1 \end{aligned}$

Put $f^{'}(x) = 0$ for extremum values

$\begin{aligned} \dfrac{a}{x}+2bx+1 & =0 \\ 2bx^2+x+a & =0 \end{aligned}$

$-1$ and $2$ are roots of this quadratic equation.

$-1+2=-\dfrac{1}{2b } \hspace{1.5mm}$ and $\hspace{1.5mm} -1\times 2= \dfrac{a}{2b}$

$\boxed{b=-\dfrac{1}{2}} \hspace{1.5mm}$ and $\hspace{1.5mm} \boxed{a=2}$

@Sambhrant Sachan , it is unnecessary to enter text in LaTex. It is difficult and the text does not flow with page width. And most importantly it is not the standard practice of Brilliant website. Since $\log$ , $\tan$ , $\cos$ are functions please put a backslash "\" in front, as you do for \frac. Let us see the differences a log |x| $a log |x|$ . Notice that all the text are in italic and stick together though I allow spaces. But a\log|x| $a\log|x|$ , only $a$ and $x$ , constant and variable are in italic, $\log$ , a function is not in italic (check $\tan$ and $\cos$ above). Also there are spaces before and after $\log$ automatically placed in. You must allow a space between function and argument, for example: \tanx $\tanx$ is an error but \tan x $\tan x$ is okay.

Chew-Seong Cheong - 4 years, 5 months ago

I changed the text , but i don't see anything wrong with the functions . i always put a backslash before a function . For e.g i have written alog|x| as a\log{|x|} : $a\log{|x|}$ and tanx as \tan{x} : $\tan{x}$ , which works perfectly.

Sabhrant Sachan - 4 years, 5 months ago

I have changed a few of your problems for you. That was why, I mentioned this here. Also Brilliant staff go round editing problems. I was appointed as a moderator.

Chew-Seong Cheong - 4 years, 5 months ago

Check out this one , I changed the $\cot x$ and $\tan x$ , and this one , I changed the $\tan$ and $\cos$ .

Chew-Seong Cheong - 4 years, 5 months ago

@Chew-Seong Cheong – These are not my problems. The problems are posted by 'subhamkar Ayare' .

Sabhrant Sachan - 4 years, 5 months ago

@Sabhrant Sachan – Sorry, I mixed up.

Chew-Seong Cheong - 4 years, 5 months ago

@Shubhamkar Ayare

Sabhrant Sachan - 4 years, 5 months ago

@Sambhrant Sachan @Chew-Seong Cheong

I will take care henceforth (and correct/modify if any mess is left behind in previously posted problems). Thank you for informing.

Shubhamkar Ayare - 4 years, 5 months ago

Thanks for understanding. All for the good of Brilliant. Wishing you a happy 2017.

Chew-Seong Cheong - 4 years, 5 months ago

IIT JEE 1983 Maths - MCQ Question 3

In case you are preparing for IIT JEE, you may want to try IIT JEE 1983 Mathematics Archives .

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