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Let f(x)=min(x^(3),x^(4))"for all "x in ...

Let f(x)=`min(x^(3),x^(4))"for all "x in R`. Then,

A

f(x) is continuous for all x

B

f(x) is indifferentiable for all x

C

`f'(x)=3x^(2)"for all "x gt 1`

D

f(x) is not differentiable at two points

Text Solution

Verified by Experts

The correct Answer is:
A
The graph, of f(x) is shown in Fig. 9 by the continuous curve.
We have `f(x)={{:(,x^(3),x le 0),(,x^(4),0 le x le 1),(,x^(3),x ge 1):}`
Clearly, f(x) is everywhere continuous. Also, f(x) is everywhere differentiable except at x=1

`therefore f'(x)={{:(,3x^(2),x le 0),(,4x^(3),0 le x lt 1),(,3x^(2),x gt1):}`
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