Question

Let f(x) =ecos x and slope of the curve y = f(x) is maximum at x = a then a equals​

Answer 1

Answer:

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

hope you like it

please rate the answer

Step-by-step explanation: