PUC Karnataka Science Class 12Department of Pre-University Education, Karnataka
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Solution for If X = 2at, Y = At2, Where a is a Constant, Then Find D 2 Y D X 2 at X = 1 2 ? - PUC Karnataka Science Class 12 - Mathematics

ConceptSimple Problems on Applications of Derivatives

Question

If x = 2aty = at2, where a is a constant, then find $\frac{d^2 y}{d x^2} \text { at }x = \frac{1}{2}$ ?

Solution

Here,

$x = 2\text { at and y } = a t^2$
$\text { Differentiating w . r . t . t, we get }$
$\frac{d x}{d t} = 2\text { a and} \frac{d y}{d t} = 2\text { at }$
$\therefore \frac{d y}{d x} = \frac{2at}{2a} = t$
$\text { Differentiating again w . r . t . t, we get}$
$\frac{d^2 y}{d x^2} = 1 \times \frac{dt}{dx} = \frac{1}{2a}$
$\text { Now,} \left[ \frac{d^2 y}{d x^2} \right]_{x = \frac{1}{2}} = \frac{1}{2a}$

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Solution If X = 2at, Y = At2, Where a is a Constant, Then Find D 2 Y D X 2 at X = 1 2 ? Concept: Simple Problems on Applications of Derivatives.
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