BUS 111 Lecture 1: BUS111_0005_11-16-15
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Def: let f be a function defined on some interval, [a,b], and let c be an x value in that interval. F(c) is an absolute maximum if f(c) f(x) for any other x value. F(c) is an absolute minimum if f(c) f(x) for any other x value. If f is a continuous function on a closed interval, [a,b], then f has both an absolute max and absolute min occurring somewhere on [a,b]. Note: to find absolute extreme, we plug into the original function. To find local extrema, we plug into the derivative. Example: find the absolute extrema of f(x)=x3-3x+1 on the interval [-3,1. 5] Answer: abs. max at (-1,3). abs min at (-3,-17) Example: find the absolute extrema for g(x)= (2x2-18)/(x) on (1, ) No critical values, skip step 3. x2 1. Example: if the profit for hot dog rolls is given by p(x)=-1/2x2+400x-5,000 , find the point of sales that provides the maximum average profit on (0,600).
