Question

6. If y = ax2 + b, then dy/dx at x = 2 is equal to
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Answer 1

SOLUTION

GIVEN

$\displaystyle \sf{y = a {x}^{2} + b }$

TO DETERMINE

$\displaystyle \sf{ \frac{dy}{dx} \: \: at \: \: x = 2}$

EVALUATION

$\displaystyle \sf{ y = a {x}^{2} + b }$

Differentiating both sides with respect to x

$\displaystyle \sf{ \frac{dy}{dx} = 2ax + 0\: }$

$\displaystyle \sf{ \implies \: \frac{dy}{dx} = 2ax \: }$

Now

$\displaystyle \sf{ \frac{dy}{dx} \bigg|_{x = 2} = 2a \times 2\: }$

$\displaystyle \sf{ \implies \: \frac{dy}{dx} \bigg|_{x = 2} =4a}$

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