Mean Value Theorem

Question

a.) Verify that the hypotheses of the Mean Value Theorem are satisfied for each of the functions on the given interval, and b.)find the value of "c" which Mean Value Theorem guarantees.

 

??(??)=4−√?? ???? [1,9]

Answer 1

I can't see the function, but the mean value says that if the function (f) is continuous (no holes or jumps) on a closed interval,[1,9] , then the slope of the secant line, (f(9)-f(1))/(9-1) is equal to the derivative somewhere on that interval.  In other words, if the function is continuous, plug 9 and 1 into the function to get f(9) and f(1).  Calculate (f(9)-f(1))/(9-1) and set that equal to the derivative, f'(c).  Finally solve for c.  It should be between 1 and 9.