Using the principle of the mean-value theorem on the indicated interval, how do you find all numbers c that satisfy the conclusion of the theorem #f(x)= 6 cos (x)#; [-pi/2, pi/2]?
1 Answer
Jan 20, 2017
Please see below.
Explanation:
There is no "using the priciple of the mean-value theorem" (whatever that means) involved.
Write down what the conclusion of the theorem says:
There is a
#f'(c) = (f(pi/2)-f(-pi/2))/(pi/2-(-pi/2))#
Now do the calculus, algebra, and trigonometry needed to find
We can see that
and
So you need to solve
The only solution in the interval is