Use the Mean Value Theorem to prove that there is a point c in the interval
[8,10] such that the line tangent to the graph of
f (x) = x^2-18x+81 at c is
horizontal.
Can we use the same theorem to say the same about the function
g(x) = |x-9| ?

Question

Use the Mean Value Theorem to prove that there is a point c in the interval
[8,10] such that the line tangent to the graph of   
f (x) = x^2-18x+81 at c is
horizontal.
Can we use the same theorem to say the same about the function
g(x) = |x-9| ?

amriju · Answer

the first curve is continous in [8,10] and diffntiabl in (8,10)...also f ( 8)=f(10)....so apply rolles theorem....then we have at a point c...f'(c)=0...that means at point c....the tangent to f(x) is horizontal....
g(x) is not diffentiable at x=9...due to a sharp edge in the graph...so cant apply rolles here