Find the maximum or minimum value of the function ft 5 160

Find the maximum or minimum value of the function. f(t) = -5 + 160t - 10t^2 Is this a maximum or minimum value? maximum value minimum value Find the maximum or minimum value of the function. g(x) - 100x^2 - 1500x maximum value minimum value Find the maximum or minimum value of the function. f(x) = 8 - x - 1/2x^2 f(x) = Is this a maximum or minimum value? maximum value minimum value

Solution

f(t) = -5 + 160t - 20t^2

it has a maximum value since the leading coefficient of the function is negative

maximum value occur at t = -b/2a

t = -160 / 2*-20 = 4

plugging t = 4 in the function

f(t) = -5 + 160(4) - 20(4)^2

maximum value = 315

2) g(x) = 100x^2 -1500 x

the function has minimum since leading coefficient is positive

minimum occurs at x = -b/2a = 1500/2*100 = 7.5

minimum value = 100(7.5)^2 -1500(7.5)^2 = -5625

3) f(x) = 8-x -1/2x^2

finction has a maximum value as leading coefficient is negative

maximum value occurs at x = 1 / 2*-1/2 = -1

maximum value = 8.5