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# If t is a real number

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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
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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! !

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