R D Sharma Solutions for Chapter: Mean Value Theorems, Exercise 1: MULTIPLE CHOICE QUESTIONS (MCQs)

If $4a+2b+c=0,$ then the equation $3a{x}^2+2bx+c=0$ has at least one real root lying in the interval.

For the function $f\left(x\right)=x+\frac{1}{x}, x\in \left[1,3\right]$, the value of $c$ for the Lagrange's Mean Value Theorem is

If from Lagrange's mean value theorem, we have $f^{\text{'}}\left(x_1\right) =\frac{f\left(b\right)-\mathrm{f}\left(a\right)}{b-a},$ then

Rolle's theorem is applicable in case of $\varphi \left(x\right)=a^{\sin x}, a>0$ in

The value of $c$ in Rolle's theorem when $f\left(x\right)=2x^3-5x^2-4x+3$, is $x\in \left[\frac{1}{3},3\right]$

When the tangent to the curve $y=x\log x$ is parallel to the chord joining the points $(1,0)$ and $(e,e)$, the value of $x$ is

The value of $c$ in Rolle's theorem for the function $f\left(x\right)=x^3-3x$ in the interval $\left[0, \sqrt{3}\right]$ is 

If $\mathrm{f}\left(\mathrm{x}\right)={\mathrm{e}}^{\mathrm{x}}\sin \mathrm{x} \mathrm{in} \left[\mathrm{o},\mathrm{\pi }\right],$ then $c$ in Rolle's theorem is