LaddiusMaximus
  • LaddiusMaximus
Find a point c satisfying the conclusion of the Mean Value Theorem for the following function and interval. f(x)=x^(-2) [1,5]
Mathematics
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
LaddiusMaximus
  • LaddiusMaximus
I know to use f(b)-f(a)/b-a becomes (1/5-1/1)/(4)
LaddiusMaximus
  • LaddiusMaximus
which equals -16/5
LaddiusMaximus
  • LaddiusMaximus
im lost after this

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More answers

Zarkon
  • Zarkon
\[f(5)=5^{-2}=\frac{1}{25}\]
Zarkon
  • Zarkon
you need to solve \[\frac{f(5)-f(1)}{5-1}=f'(c)\] for \(c\)
LaddiusMaximus
  • LaddiusMaximus
still lost
experimentX
  • experimentX
find dy/dx ... put it to the value calculated from above and solve for x
experimentX
  • experimentX
dy/dx = ((1/25) - 1)/(5-1) ... solve for x
experimentX
  • experimentX
c = http://www.wolframalpha.com/input/?i=-2x%5E-3+%3D+-24%2F100
experimentX
  • experimentX
2.0374 (( [1, 5]
anonymous
  • anonymous
\[ \frac{f[5]-1}{5-1}= f'[c] \] \[ -\frac{6}{25}= -\frac 2 {c^3} \] \[3 c^3= 25 \] \[c = (\frac {25}3)^{1/3}\]

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