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

Guest Oct 25, 2020

#1**+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!

!

asinus Oct 25, 2020

#4**+1 **

Without calculus:

this is a dome shaped parabola (due to the -1 coefficient of t^{2})

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 **

ElectricPavlov Oct 25, 2020