# Q1  Verify Rolle’s theorem for the function

According to Rolle's theorem function must be
a )  continuous in given closed interval say [x,y]
b ) differentiable in given open interval say (x,y)
c ) f(x) = f(y)
Then their exist a   such that
If all these conditions are satisfies then we can verify  Rolle's theorem
Given function is

Now, being a polynomial function,   is both continuous in [-4,2] and differentiable in (-4,2)
Now,

Similalrly,

Therefore, value of  and  value of f(x) at -4 and 2 are equal
Now,
According to roll's theorem their is point c ,  such that
Now,

And
Hence, Rolle's theorem is verified for the given function

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