BITSAT 2015 Paper

Let m be the slope of the tangent to the curve
y = ex cos x
Then , m =

dy

dx

= ex (cos x - sin x)
Diff. w.r.t ‘x’
⇒

dm

dx

= ex (cos x - sin x) + ex (- sin x - cos x) = - 2ex sin x
and

d2m

dx2

= - 2ex (sin x + cos x)
Put

dm

dx

= 0 ⇒ sin x = 0 ⇒ x = 0 , π , 2π
Clearly,

d2m

dx2

> 0 for x = π
Thus, y is minimum at x = π.
Hence the value of α = π