Maximum And Minimum Values - An Approach To Calculus
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An Approach to C A L C U L U S Table of Contents | Home 10 MAXIMUM AND MINIMUMVALUESThe turning points of a graph
WE SAY THAT A FUNCTION f(x) has a relative maximum value at x = a, if f(a) is greater than any value immediately preceding or follwing. We call it a "relative" maximum because other values of the function may in fact be greater. We say that a function f(x) has a relative minimum value at x = b, if f(b) is less than any value immediately preceding or follwing. Again, other values of the function may in fact be less. With that understanding, then, we will drop the term relative. The value of the function, the value of y, at either a maximum or a minimum is called an extreme value. Now, what characterizes the graph at an extreme value?
The tangent to the curve is horizontal. We see this at the points A and B. The slope of each tangent line -- the derivative when evaluated at a or b -- is 0. f '(x) = 0. Moreover, at points immediately to the left of a maximum -- at a point C -- the slope of the tangent is positive: f '(x) > 0. While at points immediately to the right -- at a point D -- the slope is negative: f '(x) Tag » How To Find Relative Maximum
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