Question

Find the point C guaranteed by the mean value theorem for f(x)? 1 MEDAL & FAN

f(x)=(x+3)/x on the interval [1,6].

so a=1 and b=6
f(1)=4 and f(6)=3/2

after this part i don't know what to do.

Answer 1

You know what mean value theorem states?

Answer 2

If you don't, then first check it.
if you do, then find the slope of the cord between (1,4) and (6,3/2)
then find derivative of f(x), set it equal to the slope you found previously and solve for x. That's it

Answer 3

so -1/2=3/x^2??

Answer 4

slope=\(\large\frac{3/2-4}{6-1}=-1/2\)
derivative=\(\large\frac{-3}{x^2}\)
so:
\(3/x^2=1/2\) or x^2=6
so \(x=\pm \sqrt{6}\)

Answer 5

of course you only want the positive root, because you want x on the interval [1,6].

Answer 6

thanks guys