Calculus Fundamentals Explained by Samuel Horelick

Author:Samuel Horelick
Language: eng
Format: epub
Tags: integration, function, calculus, derivatives, differentiation, integrals, chain rule, limit, continuity, area, maximum, minimum, inflection, algebra, trigonometry, logarithms
Publisher: Samuel Horelick

To find these intervals we must find points for which the derivative of the function is equal to zero. The derivative of f(x) = 2x3 + 3x2 _ 12x + 1 is 6x2 + 6x _ 12 = 6(x2 + x _ 2) = 6(x + 2)(x _ 1). The derivative is zero when 6(x + 2)(x _ 1)= 0, which means that (x + 2) = 0 or (x _ 1) = 0, x = _ 2 or x = 1. Therefore, the intervals are: (_ µ, _ 2), (_ 2, 1) and (1, µ).

1. Arbitrarily select any number x in each interval

2. Plug this number into the derivative to see if the derivative is positive or negative:

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