Question types

Mean Value Theorems question types

82 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.

82
Questions
4
Question groups
5
Question types
Sample Questions

Mean Value Theorems questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

If 4a + 2b + c = 0, then the equation 3ax2 + 2bx + c = 0 has atleast one real root lying in the interval:
  1. (0, 1)
  2. (1, 2)
  3. (0, 2)
  4. None of these.
View full solution
For the function $\text{f}(\text{x})=\text{x}+1\text{x},\text{x}\in[1,3],$ the value of c for the Lagrange's mean value theorem is:
  1. 1
  2. $\sqrt3$
  3. 2
  4. none of these
View full solution
The value of c in Rolle's theorem for the function $\text{f}(\text{x})=\frac{\text{x}(\text{x}+1)}{\text{e}^{\text{x}}}$ defined on [-1, 0] is:
  1. $0.5$
  2. $\frac{1+\sqrt5}{2}$
  3. $\frac{1-\sqrt5}{2}$
  4. $-0.5$
View full solution
When the tangent to the curve $\text{y}=\text{x}\log\text{x}$ is parallel to the chord joining the points (1, 0) and (e, e), the value of x is:
  1. $\text{e}^{\frac{1}{1}-\text{e}}$
  2. $\text{e}^{(\text{e}-1)(2\text{e}-1)}$
  3. $\text{e}^{\frac{2\text{e}-1}{\text{e}-1}}$
  4. $\frac{\text{e}-1}{\text{e}}$
View full solution
The value of c in Rolle's theorem when
f(x) = 2x3 - 5x2 - 4x + 3, $\text{x}\in\Big[\frac{1}{3},3\Big]$ is:
  1. $2$
  2. $-\frac{1}{3}$
  3. $-2$
  4. $\frac{2}{3}$
View full solution
Q 62 Marks2 Marks
Discuss the applicability of the Rolle's theorem for the following function on the indicated interval
$\text{f}(\text{x})=\sin\frac{1}{\text{x}}\text{ for}-1\leq\text{x}\leq1$
View full solution
Q 72 Marks2 Marks
Discuss the applicability of the Rolle's theorem for the following function on the indicated interval
$\text{f}(\text{x})=2\text{x}^2-5\text{x}+3\text{ on }[1,3]$
View full solution
Q 83 Marks3 Marks
Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point 'c' in the indicated interval as stated by the Lagrange's mean value theorem.
$\text{f}(\text{x})=\sqrt{\text{x}^2-4}\text{ on }[2,4]$
View full solution
Q 93 Marks3 Marks
Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point 'c' in the indicated interval as stated by the Lagrange's mean value theorem.
f(x) = x2 + x - 1 on [0, 4]
View full solution
Q 103 Marks3 Marks
Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point 'c' in the indicated interval as stated by the Lagrange's mean value theorem.

$\text{f}(\text{x})=\sin\text{x}-\sin2\text{x}-\text{x}\text{ on }[0,\pi]$

View full solution
Q 113 Marks3 Marks
Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point 'c' in the indicated interval as stated by the Lagrange's mean value theorem.
f(x) = 2x2 - 3x + 1 on [1, 3]
View full solution
Q 123 Marks3 Marks
Show that the Lagrange's mean value theorem is not applicable to the function
$\text{f}(\text{x})=\frac{1}{\text{x}}\text{ on }[-1,1]$
View full solution
Q 134 Marks4 Marks
Verify Rolle's theorem for the following function on the indicated intervals

f(x) = (x - 1) (x - 2)2 on [1, 2]

View full solution
Q 154 Marks4 Marks
Verify Rolle's theorem for the following function on the indicated intervals

f(x) = x(x - 4)2 on the interval [0, 4]

View full solution
Q 164 Marks4 Marks
Verify Rolle's theorem for the following function on the indicated intervals

$\text{f}(\text{x})=\cos2\Big(\text{x}-\frac{\pi}{4}\Big)\text{ on }\Big[0,\frac{\pi}{2}\Big]$

View full solution
Q 174 Marks4 Marks
Verify Lagrange's mean value theorem for the following function on the indicated intervals. find a point 'c' in the indicated interval as stated by the Lagrange's mean value theorem.
$\text{f}(\text{x})=\tan^{-1}\text{x}\text{ on }[0,1]$
View full solution

Generate a Mean Value Theorems paper free

Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.

Download App