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Question

Mathematics Question on Continuity and differentiability

If y=ax2+by = ax^2 + b, then dydx\frac{dy}{dx} at x=2x = 2 is equal to

A

4a4a

B

3a3a

C

2a2a

D

none of these

Answer

4a4a

Explanation

Solution

We have, y=ax2+by=ax^{2}+b dydx=2ax\Rightarrow \frac{dy}{dx}=2ax dydxx=2=2a×2=4a\frac{dy}{dx} \bigg|_{x=2}= 2a \times 2 = 4a