Question:
The value of \( x \) in the interval \( [4, 9] \) at which the function
\[
f(x) = \sqrt{x}
\]
\text{satisfies the mean value theorem is:}
The value of \( x \) in the interval \( [4, 9] \) at which the function
\[
f(x) = \sqrt{x}
\]
\text{satisfies the mean value theorem is:}
Show Hint
The mean value theorem states that there exists a point where the derivative equals the average rate of change.
Updated On: Jan 12, 2026
- \( \frac{13}{4} \)
- \( \frac{17}{4} \)
- \( \frac{21}{4} \)
- \( \frac{25}{4} \)
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Using the mean value theorem, calculate the derivative of \( f(x) \) and solve for \( x \) in the interval \( [4, 9] \).
Final Answer: \[ \boxed{\frac{17}{4}} \]
Final Answer: \[ \boxed{\frac{17}{4}} \]
Was this answer helpful?
0
0
Top VITEEE Mathematics Questions
- The product of all values of $(\cos \alpha + i \sin \alpha)^{3/5}$ is equal to
- A football is inflated by pumping air in it. When it acquires spherical shape its radius increases at the rate of 0.02 cm/s. The rate of increase of its volume when the radius is 10 cm is ___________$\pi$ cm/s
- The interval in which the function $f\left(x\right) = \frac{4x^{2}+1}{x}$ is decreasing is :
- If the normal to the curve $y = f(x)$ at $(3,4)$ makes an angle $\frac{3 \pi}{4}$ with the positive x-axis, then $f'(3)$ is equal to
- The principal value of $sin^{-1} \left(sin \frac{5\pi}{3}\right)$ is
View More Questions
Top VITEEE Applications of Derivatives Questions
- The equation of the tangent to the curve \(y=x^3-2x+1\) at \((1,0)\) is:
- A boat takes 4 hours to travel 40 km downstream and 6 hours to return. The speed of the stream is:
- A spherical balloon is expanding. If the radius is increasing at the rate of 2 centimeters per minute, the rate at which the volume increases (in cubic centimeters per minute) when the radius is 5 centimeters is
- The function \(f(x)=x^3+ax^2+bx+c\), \(a^2\leq 3b\) has
- The two curves \(y=3^x\) and \(y=5^x\) intersect at an angle
View More Questions
Top VITEEE Questions
- A motor of power $P_0$ is used to deliver water at a certain rate through a given horizontal pipe. To increase the rate of flow of water through the same pipe $n$ times, the power of the motor is increased to $P_1$. The ratio of $P_1 $ to $P_0$ is
- A $30\,V-90\,W$ lamp is operated on a $120\,V$ DC line. A resistor is connected in series with the lamp in order to glow it properly. The value of resistance is
- Which of the following is not a characteristic of transition elements ?
- Most crystals show good cleavage because their atoms, ions or molecules are
- Which of the following sets consists only of essential amino acids ?
View More Questions