<p>Can anyone help me with this?</p>
<p>The function f(x) is defined as f(x)=-2(x+2)(x-1)^2 on the open interval (-3,3). The function g(x) is defined as the absolute value of f(x) in the open interval (-3,3). Determine the coordinates of the relative maxima of g(x) in the open interval. Explain your reasoning.</p>
<p>Thanks</p>
<p>(x divided by absolute value of x) times (derivative of x) x cannot equal 0</p>
<p>g(x) is zero at -2 and 1, and otherwise positive, so these are (absolute) minima, and by continuity there must be a relative maximum between these values. g(x) = 2(x-1)^2*abs(x+2) so it is not differentiable at -2; for x > -2, it equals 2(x+2)(x-1)^2, however, which is differentiable. The derivative works out to 6(x^2 - 1) which has zeroes at + and -1. The zero at -1 is the relative maximum; g(-1) = 8.</p>