Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 5 + 54x − 2x3, [0, 4]

The absolute maximum and minimum of on are 113 and 5.

Step-by-step explanation:

Let be , the first and second derivatives of the function are, respectively:

Now, let equalize the first derivative to zero and solve the resulting expression:

According to the given interval, only is a valid outcome. Lastly, this is evaluated in the second derivative expression:

leads to an absolute maximum.

The absolute minimum is determined by evaluating at each extreme of the interval:

The absolute maximum and minimum of on are 113 and 5.

(x+3)(x+7)

step-by-step explanation: