Sender: corrie hi! i have a question i was hoping you could help me with! I need to find if the mean value theorem exists. and if so, find all values c guaranteed by the theorem. f(x) = x^{2}25 on the interval [10,0] thanks for your time and help!
corrie For the Mean Value Theorem to apply you need f(x) differentiable in the interval (10, 0). My first thought is to sketch the graph of the function y = x^{2}25 When you take the absolute value of the yvalues to get the function f(x), the negative yvalues become positive. Thus the part of the graph below the Xaxis gets "turned over" and the graph becomes y = x^{2}25 At the point (5, 0), which is inside the interval (10, 0) the curve clearly has no tangent line. Thus y = f(x) is not differentiable at x = 5 and thus the Mean Value Theorem does not apply. Cheers,Harley
