Question

Find a point c satisfying the conclusion of the Mean Value Theorem for the following function and interval.
f(x)=x^(-2) [1,5]

Answer 1

I know to use f(b)-f(a)/b-a becomes (1/5-1/1)/(4)

Answer 2

which equals -16/5

Answer 3

im lost after this

Answer 4

\[f(5)=5^{-2}=\frac{1}{25}\]

Answer 5

you need to solve \[\frac{f(5)-f(1)}{5-1}=f'(c)\] for \(c\)

Answer 6

still lost

Answer 7

find dy/dx ... put it to the value calculated from above and solve for x

Answer 8

dy/dx = ((1/25) - 1)/(5-1) ... solve for x

Answer 9

c = http://www.wolframalpha.com/input/?i=-2x%5E-3+%3D+-24%2F100

Answer 10

2.0374 (( [1, 5]

Answer 11

\[ \frac{f[5]-1}{5-1}= f'[c]
\]

\[ -\frac{6}{25}= -\frac 2 {c^3}
\]
\[3 c^3= 25
\]

\[c = (\frac {25}3)^{1/3}\]