9Q20. Determine the open intervals on which the function y = f(x) = 3x^4 - 4x^3

Question

9Q20. Determine the open intervals on which the function y = f(x) = 3x^4 - 4x^3 - 12x^2 + 5 is increasing and those intervals on which it is decreasing. 1/ (z) 12x (z - 2) (z + 1) dx Critical Numbers: x1 = ; x2 = ; x3 = ; TRUE OR FALSE f(x) is increasing on (- infinity, -1). TRUE OR FALSE f(x) is increasing on (-1, 0). TRUE OR FALSE f(x) is increasing on (0, 1). TRUE OR FALSE f(x) is increasing on (1, infinity). TRUE OR FALSE f(x) has a relative (local) maximum at x = -1. TRUE OR FALSE f(x) has a relative (local) maximum at x = 0. TRUE OR FALSE f(x) has a relative (local) maximum at x = 2.

Explanation / Answer

1) The critical points are x =0,-1,2
2) a) False
b) True
c) False
d) False
e) False
f) True
g) False

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