# In a curve y = t2 + 2t and x = t3, find the slope $\rm dy\over dx$ at t = 5

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In a curve y = t2 + 2t and x = t3, find the slope $\rm dy\over dx$ at t = 5
1. $\rm \frac{4}{5}$
2. $\rm \frac{4}{3}$
3. $\rm \frac{12}{5}$
4. $\rm \frac{4}{25}$
5. None of these

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Correct Answer - Option 4 : $\rm \frac{4}{25}$

Concept:

Parametric Form:

If f(x) and g(x) are the functions in x, then

$\rm df(x)\over dg(x)$ = $\rm \frac{df(x)\over dx}{dg(x)\over dx}$

Calculation:

Given y = t2 + 2t

$\rm {dy\over dt}$ = 2t + 2

Also x = t3

$\rm dx\over dt$ = 3t2

Now $\rm dy\over dx$ = $\rm \frac{dy\over dt}{dx\over dt}$

$\rm dy\over dx$ = $\rm \frac{2t +2}{3t^2}$

At t = 5,

$\rm {dy\over dx}$ = $\rm \frac{2(5) +2}{3(5)^2}$ = $\rm \frac{4}{25}$