Ques. -19

Calculus Level 3

If $y=a \log x+bx^2+x$ has extremum value at $x=1$ and $x=2$ , what is $(a,b)$ ?

\left(\frac{1}{2},2\right)

\left(-\frac{2}{3}, -\frac{1}{6}\right)

\left(2,-\frac{1}{2}\right)

\left(1,\frac{1}{2}\right)

2 solutions

Sandeep Rathod
Feb 25, 2015

$y=a \cdot logx+b \cdot x^2+x$

$\dfrac{d}{dx} = \dfrac{a}{x} + 2bx + 1$

$a + 2b + 1 =0$

$\dfrac{a}{2} + 4b + 1 = 0$

$(\frac{-2}{3},\frac{-1}{6})$

How to draw its graph?

Shouldn't $\frac{dy}{dx}=\frac{a}{x\ln{10}}+2bx+1$ ?

Omkar Kulkarni - 6 years, 1 month ago

Omur Faruque
Jul 9, 2015

It should have been made clear in the question that logx is being used as natural logarithm. Please, edit the question.