Find the absolute maximum value of the function fx 4x e Sol

Find the absolute maximum value of the function f(x)- 4x - e*

Solution

To obtain maximum value of the function f(x) we differentiate the function w.r.t x

f(x) = 4(x-e^x )

df(x)/dx = 4(1 - e^x) = 0

    1-e^x = 0

1 = e^x

^{log 1 = x* loge}

^{---> x = 0}

Therefore the given function has maximum value at 0

f(4) = 4(0-1) = -4

Since we need to take absolute value |f(x)| = |-4| = 4