If t is a real number

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!

  !

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