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BITSAT 2015 Paper

Section: Mathematics

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Question : 106 of 150

Marks: +1, -0

The slope of the tangent to the curve y =

e^x

cos x is minimum at x = α, 0 ≤ a ≤ 2π, then the value of a is

0
π
2π
3π/2

Solution:

Let m be the slope of the tangent to the curve

y =

e^x

cos x

Then , m =

\frac{dy}{dx}

=

e^x

(cos x - sin x)

Diff. w.r.t ‘x’

⇒

\frac{dm}{dx}

=

e^x

(cos x - sin x) +

e^x

(- sin x - cos x) = -

2e^x

sin x

and

\frac{d^2 m}{dx^2}

= -

2e^x

(sin x + cos x)

Put

\frac{dm}{dx}

= 0 ⇒ sin x = 0 ⇒ x = 0 , π , 2π

Clearly,

\frac{d^2 m}{dx^2}

> 0 for x = π

Thus, y is minimum at x = π.

Hence the value of α = π

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