Question:
If $y = ax^2 + b$, then $\frac{dy}{dx}$ at $x = 2$ is equal to
If $y = ax^2 + b$, then $\frac{dy}{dx}$ at $x = 2$ is equal to
Updated On: Jul 6, 2022
- $4a$
- $3a$
- $2a$
- none of these
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The Correct Option is A
Solution and Explanation
We have, $y=ax^{2}+b$
$\Rightarrow \frac{dy}{dx}=2ax$
$\frac{dy}{dx} \bigg|_{x=2}= 2a \times 2 = 4a$
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Notes on Continuity and differentiability
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.