Given the function #f(x)=x(x^2-x-2)#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [-1,1] and find the c?
first of all, the Mean Value theorem isn't an hypothesis, it is a theorem which states that if a function is continuous over an interval
and since this function is continuous over all values
, we know that there does exist such a value c, all we have to do is find it
the derivative of this function can be found fairly simply by just using the power rule and the derivative is
therefore, to find c,
and on solving this equation using the quadratic formula
but since c should be such that