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Consider the graph of the function f(x) ...

Consider the graph of the function `f(x) = x+ sqrt|x|` Statement-1: The graph of `y=f(x)` has only one critical point Statement-2: `fprime (x)` vanishes only at one point

A

Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 2 is a correct explanation for Statement 1.

B

Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.

C

Statement 1 is true, Statement 2 is false.

D

Statement 1 is false, Statement 2 is true.

Text Solution

Verified by Experts

The correct Answer is:
D
`f(x)={{:(x+sqrtx,"if",ge0),(x+sqrt(-x),"if",xlt0):}`
The graph of f(x) is shown with `f'(x)=0` as `x=-1//4`. Also derivative fails at x = 0. Hence there are two cirtical points.
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