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If t is a real number, what is the maximum possible value of the expression -t^2 + 18t - 4?

 Oct 25, 2020
 #1
avatar+10583 
+1

If t is a real number, what is the maximum possible value

of the expression  - t^2 + 18t - 4 ?

 

Hello Guest!

 

\(f(t)= -t^2 + 18t - 4\\ \frac{df(t)}{dt}=-2t+18=0\\ -2t=-18\)

\(t=9\)

\(f(t)= -t^2 + 18t - 4=-9^2+18\cdot 9-4\\ \color{blue}f(t)_{max}=77\)

 

 

\(The\ maximum\ possible\ value\)

\(of\ the\ Expression\ {\color{BrickRed}[ -t^2 + 18t - 4]}\ \color{blue} is\ 77.\) 

Thanks anonymus!

laugh  !

 Oct 25, 2020
edited by asinus  Oct 25, 2020
edited by asinus  Oct 25, 2020
 #2
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0

Doesn't deserve the +1 like, the maximum value occurs when t = 9, but it isn't equal to 9.

Guest Oct 25, 2020
 #3
avatar+10583 
0

Hello guest from answer  #2.
You're right, the maximum value of the function is not 9. I'll correct it.
Thanks for the hint.
greeting

asinus  Oct 25, 2020
 #4
avatar+28021 
+1

Without calculus:

  this is a dome shaped parabola (due to the -1 coefficient of t2)

    maximum value will occur at the vertex  t value of  - b/2a = - 18 / (2*-1)  = t=9

       this is th maximum t     

             since this is a function of 't' you will need to sub in this value of t into the equation to calulate the maximum value of the function             

    -9^2 + 18(9) - 4 = 77

 Oct 25, 2020

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