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)
1
Expert's answer
2011-03-15T09:20:06-0400
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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