Question

Find both the maximum value and the minimum value of

3x⁴ − 8x³ + 12x² − 48x + 25 on the interval [0, 3]

Answer 1

Let f(x) = 3x⁴ − 8x³ + 12x² − 48x + 25.

Now,gives x = 2 or x²+ 2 = 0 for which there are no real roots.

Therefore, we consider only x = 2 ∈[0, 3].

Now, we evaluate the value of f at critical point x = 2 and at the end points of the interval [0, 3].

Hence, we can conclude that the absolute maximum value of f on [0, 3] is 25 occurring at x = 0 and the absolute minimum value of f at [0, 3] is − 39 occurring at x = 2.