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The function f(x)=x(x+3)e^-(1/2)x satisfies all the condition of of rolles theoram in [-3,0].The value of c is

7 years ago

Pratham Ashish
17 Points

hi,

If a real-valued function ƒ is continuous on a closed interval [ab], differentiable on the open interval (ab), and ƒ(a) = ƒ(b), then there exists a c in the open interval (ab) such that

$f'(c) = 0.\,$

so differentiating given f(x) with respect to x, we get

(x+3)e^-(1/2)x + x*e^-(1/2)x - (0.5) x(x+3)e^-(1/2)x = 0

taking e^-(1/2)x common ,then we will left with

(x+3) + x - (0.5) x(x+3) = 0

after solving this eqn in x ,u will get

x=3, x = -2

since for validation of rolles theorem this value of x shud lie in the given interval

c = -2..................

7 years ago
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