NDA 2017 Maths · Mathematics · Continuity and Differentiability · hard

Let f(x)=x^2 for x≤1 and f(x)=ax+b for x>1. If f is differentiable at x=1, then b equals

Single correct option

Let

f(x)=x^2

for

x\le1

and

f(x)=ax+b

for

x>1

. If

f

is differentiable at

x=1

, then

b

equals

Show answer and solution

Answer: (C) $-1$

Continuity gives

a+b=1

. Differentiability needs equal slopes:

a=2

(the derivative of

x^2

1

). Hence

b=1-2=-1

. The value

1

a+b

, which continuity alone gives, and

2

a

Original question written in the NDA 2017 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake