Question

Can anyone help me with this problem, Find all points guaranteed by the mean value theorem for the closed interval given

f(x)= 1/x, [1,4]

Answer 1

mvt says there is a number in the interval [a,b] with \(f'(c)=\frac{f(b)-f(a)}{b-a}\)
replace a by 1, b by 4, \(f(x)\) by \(\frac{1}{x}\) and \(f'(x)\) by \(-\frac{1}{x^2}\)

Answer 2

you get
\[-\frac{1}{x^2}=\frac{\frac{1}{4}-\frac{1}{1}}{4-1}\] and then clean this up, solve for "x"

Answer 3

Okay thank you, I ended up getting x=2 does that sound right?