Correct Answer - Option 3 :
\(\frac{{ 6}}{7}\)
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 = 2t2 - 2t - 5
\(\rm {dy\over dt}\) = 4t - 2
Also x = t2 + 3t - 8
\(\rm dx\over dt\) = 2t + 3
Now \(\rm dy\over dx\) = \(\rm \frac{dy\over dt}{dx\over dt}\)
\(\rm dy\over dx\) = \(\rm \frac{4t-2}{2t+3}\)
At t = 2,
\(\rm {dy\over dx}\) = \(\rm \frac{4(2) -2}{2(2)+3}\) = \(\rm \frac{6}{7}\)
