Question

3. The maximum slope of the tangent to the curve y=



sin x∈ [0,2]is at ​

Answer 1

Answer:

ANSWER

Let m be the slope of the tangent to the curve

y=e

x

cosx

Then, m=

dx

dy

=e

x

(cosx−sinx)

⇒

dx

dm

=e

x

(cosx−sinx)+e

x

(−sinx−cosx)=−2e

x

sinx

and

dm

2

d

2

m

=−2e

x

(sinx+cosx)

∴

dx

dm

=0

⇒sinx=0⇒x=0

clearly,

dm

2

d

2

m

<0