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) = |x2-25| on the interval [-10,0]
thanks for your time and help!
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 = x2-25
When you take the absolute value of the y-values to get the function f(x), the negative y-values become positive. Thus the part of the graph below the X-axis gets "turned over" and the graph becomes
y = |x2-25|
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,