If the minimum value of \(f(x)=\frac{5 x^2}{2}+\frac{\alpha}{x^5}, x>0\), is 14 , then the value of \(\alpha\) is equal to:
- 32
- 64
- 128
- 256
The Correct Option is C
Solution and Explanation
The correct option will be (C): 128
Top Questions on Continuity and differentiability
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\[ f(x) = \begin{cases} \sin(2x), & \text{for } x > 0, \\ a + bx, & \text{for } x \leq 0, \end{cases} \]
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Consider the following cell: $ \text{Pt}(s) \, \text{H}_2 (1 \, \text{atm}) | \text{H}^+ (1 \, \text{M}) | \text{Cr}_2\text{O}_7^{2-}, \, \text{Cr}^{3+} | \text{H}^+ (1 \, \text{M}) | \text{Pt}(s) $
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Concepts Used:
Continuity & Differentiability
Definition of Differentiability
f(x) is said to be differentiable at the point x = a, if the derivative f ‘(a) be at every point in its domain. It is given by
Definition of Continuity
Mathematically, a function is said to be continuous at a point x = a, if
It is implicit that if the left-hand limit (L.H.L), right-hand limit (R.H.L), and the value of the function at x=a exist and these parameters are equal to each other, then the function f is said to be continuous at x=a.
If the function is unspecified or does not exist, then we say that the function is discontinuous.