A curve is represented parametrically by the equations x = f ( t )= a ^ ( b ^ t ) and y =…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
A curve is represented parametrically by the equations \(\mathrm{x}=\mathrm{f}(\mathrm{t})=\mathrm{a}^{\ln \left(\mathrm{b}^{\mathrm{t}}\right)}\)and \(\mathrm{y}=\mathrm{g}(\mathrm{t})=\mathrm{b}^{-\ln \left(\mathrm{a}^{\mathrm{t}}\right)}\)a, b > 0 and a ≠ 1, b ≠ 1 where t ∈ R.
The value of \(\frac{f(t)}{f^{\prime}(t)} \cdot \frac{f^{\prime \prime}(-t)}{f^{\prime}(-t)}+\frac{f(-t)}{f^{\prime}(-t)} \cdot \frac{f^{\prime \prime}(t)}{f^{\prime}(t)} \forall t \in R,\)is equal to
- –2
- 2
- –4
- 4
Answer
(A) –2
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