Find the maximum value of fx 8x2 5x 6 on the interval 20

Find the maximum value of f(x) = -8x^2 + 5x + 6| on the interval [-20, 20] maximum value is It is attained at x = 1

Solution

f(x) = -8x^2 + 5x + 6

lets find the derivative of the function f(x) that is f \'(x) and then plug

f\'(x)= 0 in order to find the point at which we attain the maxima

f\'(x) = -16x + 5

f\'(x) = -16x + 5 = 0

=> x = 5/16 = .3125

plug x = 5/16 or x = .3125 in the function f(x) to get the maximum value of the function

f(5/16) = -8(5/16)^2 + 5*(5/16) + 5 = 217/32 = 6.78125

x = .3125 lies within the interval x E [-20 , 20]

hence the maximum value is = 6.39063 . It is attained at x = .3125