- #1

Titan97

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## Homework Statement

##f(x)## is a continuous and differentiable function. ##f(x)## takes values of the form ##^+_-\sqrt{I}## whenever x=a or b, (where ##I## denotes whole numbers) ; otherwise ##f(x)## takes real values. Also, ##|f(a)|\le |f(b)|## and ##f(c)=-1.5##. Graph of ##y=f(x)f'(x)##:

The number of rational values that ##f(a)+f(b)+f(c)## can take is?

## Homework Equations

None

## The Attempt at a Solution

My teacher told me that the question has data insufficiency. But I don't know why.

##f(x)f'(x)=0## implies either ##f(x)## or ##f'(x)## or both are zero. At ##c## ##f'(x)## is zero since ##f(x)## is non zero. Hence, f(x) has a maxima or minima at ##x=c##.

Now, from ##a## to ##c##, either bothe the function and its derivative is positive or both are negative. Applying Rolle's theorem,

##{f'(k)}^2+f(k)f"(k)=0## since ##g(a)=(c)##.

But I don't seem to be getting anywhere.