mathmath333
  • mathmath333
functions
Mathematics
jamiebookeater
  • jamiebookeater
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mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} & \normalsize \text{Find the minimum value of the function}\hspace{.33em}\\~\\ & f(x)=\log_{2} (x^2-2x+5) \hspace{.33em}\\~\\ \end{align}}\)
anonymous
  • anonymous
IDK
anonymous
  • anonymous
make roots of the equation then use both roots to find the answer

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misty1212
  • misty1212
unlikely since you cannot take the log of zero
misty1212
  • misty1212
find the minimum value of the quadratic
mathmath333
  • mathmath333
roots are imaginary here
misty1212
  • misty1212
which will be the second coordinate of the vertex
misty1212
  • misty1212
vertex of \[x^2-2x+5\] should be easy enough to find
misty1212
  • misty1212
since log is an increasing function, once you find the minimum value of the quadratic, that will give you the input that produces the minimum value of the log
mathmath333
  • mathmath333
minimum is 5
misty1212
  • misty1212
no it is not
misty1212
  • misty1212
the second coordinate of the vertex is not 5, the constant is 5
mathmath333
  • mathmath333
i put x=0 here x^2-2x+5
misty1212
  • misty1212
yeah sure, if you put in 0 you get 5, but the vertex is NOT \((0,5)\)
misty1212
  • misty1212
use \[-\frac{b}{2a}\] to find the first coordinate of the vertex
ganeshie8
  • ganeshie8
whats the minimum value of \(x^2 - 10000000x + 1\) ?
misty1212
  • misty1212
plug that in to find the second coordinate ( it is definitely not 5)
anonymous
  • anonymous
yes
anonymous
  • anonymous
misty its girl like u that i study maths u are eaiutiful
misty1212
  • misty1212
thank you darling, you look pretty cute yourself
ganeshie8
  • ganeshie8
i should change my profile pic
mathmath333
  • mathmath333
oh i remember that dy/dx=0, minimum is 4
misty1212
  • misty1212
lol pick a cute girl, everyone will love you
anonymous
  • anonymous
btw can u explain it with solutionj plz
misty1212
  • misty1212
yeah min is 4 and \[\log_2(4)\] is your answer
anonymous
  • anonymous
wait let me search cute girl pics damn those are some fine kittens
misty1212
  • misty1212
you certainly don't need to use calc to find the vertex of a quadratic though...

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