TS EAMCET 11-Sep-2020 Shift 2 Solved Paper

Given that, f(x)=‌

x−1

ex

....(i)
Differentiating Eq. (i) w.r.t. x on both sides, we get
[∵‌

d

dx

(‌

u

v

)=‌

v d dx u−u dv dx

v2

]
=‌

ex⋅1−(x−1)ex

e2x

f′(x)=‌

2−x

ex

....(ii)
Putting x=0 in Eq. (ii), we get
f′(0)=‌

2−0

e0

=‌

2

1

⇒f′(0)=2 .....(iii)
Now, differentiating Eq. (ii) w.r.t. x on both sides, we get
=‌

ex(−1)−(2−x)ex

e2x

f′′(x)=‌

(x−3)

ex

....(iv)
Putting x=0, in Eq. (iv), we get
Adding Eq. (iii) and Eq. (v), we get