Given the function # f(x) = 8 sqrt{ x} + 1#, how do you determine whether f satisfies the hypotheses of the Mean Value Theorem on the interval [1,10] and find the c?
1 Answer
Please see below.
Explanation:
The Mean Value Theorem has two hypotheses:
H1 :
H2 :
A hypothesis is satisfied if it is true.
So we need to determine whether
It is.
(
and whether
It is.
(Remember that "differentiable" means the derivative exists.)
A very common way of stating the Mean Value Theorem gives the conclusion as:
There is a
A popular exercise (calculus and algebra) is to ask students to find the value or values of
To do this, find