Paul D.

asked • 09/22/18

Let f : [a, b] → R be a differentiable function and let P be a partition of [a, b]. Show that L(P, f′) ≤ f(b) − f(a).

 Let f : [a, b] → R be a differentiable function and let P be a partition of [a, b]. Show that L(P, f′) ≤ f(b) − f(a).
 
Hint: Use the Mean-Value Theorem.
(Recall that, if P = (x0,x1,...,xn), then L(P,f′) = Σmj∆xj, where mj = inf{f′(t) : t ∈
[xj−1,xj]}and∆xj =xj −xj−1 foreach1≤j≤n.)

1 Expert Answer

By:

Mark M. answered • 09/23/18

Retired math prof. Calc 1, 2 and AP Calculus tutoring experience.

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