It is given that the Rolles theorem holds for the function `f(x)=x^3+b x^2+c x ,\ \ x in [1,2]` at the point `x=4/3` . Find the values of `b` and `c` .

Explanation

Solution:

let us write conditions for applicability of Rolle’s theorem:

For a Real valued function ‘f’:

a) Function ‘f’ needs to be continuous in the closed interval [a, b].

b) Function ‘f’ needs differentiable on the open interval (a, b). c) f(a) = f(b)


Then there exists at least one c in the open interval (a, b) such that f’(c) = 0.


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