AP EAMCET · Maths · Application of Derivatives
The curve \(f(x)=e^x \sin x\) is defined in the interval \([0,2 \pi]\). The value of \(x\) for which the slope of the tangent drawn to the curve at \(x\) is maximum, is
- A \(\frac{\pi}{4}\)
- B \(\frac{\pi}{2}\)
- C \(\frac{\pi}{6}\)
- D \(\frac{\pi}{3}\)
Answer & Solution
Correct Answer
(B) \(\frac{\pi}{2}\)
Step-by-step Solution
Detailed explanation
We have, \[ f(x)=e^x \cdot \sin x \] difference w.r.t ' \(x\) ' \[ f^{\prime}(x)=e^x \cos x+e^x \sin x \] For \(f^{\prime}(x)\) is maximum we find \(f^{\prime \prime}(x)\)…
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