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Answer to Question #1917 in Calculus for Bujju

Question #1917
From the graph of f(x)=3x^4-20x^3+24x^2, identify on the interval [-1,5] the x-y coordinates of the absolute maximum.

Give your answer in the form (a,b). If there is more than one answer enter points separated by commas. For example (a,b), (c,d)
Expert's answer
Let's find the first derivative of f(x):

f'(x) = 12 x3 - 60 x2 + 48 x
12 x3 - 60 x2 + 48 x = 0
x1 = 0
x2 - 5x + 4 = 0
x2 = 4
x3 = 1
f'(x) > 0 at (0, 1) and (4,5]
f'(x) < 0 at [-1, 0) and (1,4)
x = 1 - is relative maximum
f(1) = 7
At the bounds
at f(-1) = 47
f(5) = -25
Thus the absolute maximum is (-1, 47)

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