Let f(x) =ecos x and slope of the curve y = f(x) is maximum at x = a then a equals
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Y' = e^x cosx - e^x sinx
f(x) = e^x (cosx - sinx)
f'(x) = e^x (cosx - sinx) + e^x (-sinx - cosx)
f'(x) = 0
⇒ e^x (-2sinx) =0
sinx = 0
x = 0, π, 2π
f"(x) = e^x (-2sinx) + e^x (-2cosx)
⇒ -2e^x (sinx + cosx)
f"(x) > 0
therefore, x = π
f(x) has minimum at x = π
slope of tangent of curve is minimum at x = π
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