G(1) = 2(1) + 4 = 6
g(1) = 6
Please be certain to use the symbol "^" to denote exponentiation. Your function y should be written as
y = x^3 + 3x2 - 2x + 4.
Principle: if the derivative of a function is negative on a certain x-interval, the function is decreasing on that interval. Thus, you must differentiate the given function: find dy/dx. Set this dy/dx = to 0 and solve the resulting equation for x. Set up intervals on the # line based upon your solutions.
For example, if x=-1 and x=2, then set up 3 intervals: (-infinity,-1), (-1,2), and (2, infinity). Looking at each interval separately, identify the interval or intervals on which the derivative dy/dx is negative.
This is a critically important skill in calculus and well worth the time and effort required to learn it.
