Question:medium
If \[ f(x) = \sqrt{2x + \frac{4}{\sqrt{2x}}} \] then \[ f'(2) \] is equal to:
If \[ f(x) = \sqrt{2x + \frac{4}{\sqrt{2x}}} \] then \[ f'(2) \] is equal to:
Show Hint
When a function is of the form \( f(x) = u + \frac{k}{u} \), the derivative is \( f'(x) = u' (1 - \frac{k}{u^2}) \). At the point where \( u^2 = k \), the derivative becomes zero. Here, at \( x=2 \), \( (\sqrt{2x})^2 = 4 \), which matches the constant in the numerator.
Updated On: May 1, 2026
- \( 0 \)
- \( -1 \)
- \( 1 \)
- \( 2 \)
- \( -2 \)
Show Solution
The Correct Option is A
Solution and Explanation
Was this answer helpful?
0
Top Questions on Application of derivatives
- If the function \( f(x) \), defined below, is continuous on the interval \([0,8]\), then: \[ f(x) = \begin{cases} x^2 + ax + b, & 0 \leq x < 2 \\ 3x + 2, & 2 \leq x \leq 4 \\ 2ax + 5b, & 4 < x \leq 8 \end{cases} \]
- BITSAT - 2024
- Mathematics
- Application of derivatives
- If \( x\sqrt{1 + y} + y\sqrt{1 + x} = 0 \), then find \( \frac{dy}{dx} \).
- BITSAT - 2024
- Mathematics
- Application of derivatives
- If \( y = \tan^{-1}\left( \frac{\sqrt{x} - x}{1 + x^{3/2}} \right) \), then \( y'(1) \) is equal to:
- BITSAT - 2024
- Mathematics
- Application of derivatives
- At \( x = \frac{\pi^2}{4} \), \( \frac{d}{dx} \left( \tan^{-1}(\cos\sqrt{x}) + \sec^{-1}(e^x) \right) = \)
- BITSAT - 2024
- Mathematics
- Application of derivatives
- Want to practice more? Try solving extra ecology questions todayView All Questions
