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Statement-1: If f and g are differentiab...

Statement-1: If f and g are differentiable at x=c, then min (f,g) is differentiable at x=c.
Statement-2: min (f,g) is differentiable at `x=c if f(c ) ne g(c )`

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
D
Let f(x)=x nd g(x)=`x^(2)` then,
`min (f(x),g(x))={{:(,x,x lt 0),(,x^(2),0 le x lt 1):}`
Clearly, f(x) and g(X) are differentiable at x=0. But, min [f(x),g(x)] is not differentiable at x=0.
So, statement-1 is not true. However, statement-2 is true.
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