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Math 2413 = Instructor: Adnan Said Chapter 3 Sections 3.1 and 3.2 3.1 Extrema of a Function on an Interval Definition of Extrema Let f be…
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The Extreme Value Theorem If f is continuous on a closed interval [a, b] , then f has both a minimum and a maximum on the interval. Find…
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Definition of Relative Extrema The graph of a typical function may have "peaks" or "valleys". Peaks and valleys are sometimes called…
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Find the critical numbers for the function. 4) £(x) = 2 sin x - cos 2x on the interval (0, 27]. 4) f (x) =2 cos x - (-2 sin 2x) = 2 cos x +…
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Find the location of the extrema of the function. 6) f(x) = 2x - 3x2/3 on the interval [-1, 3}. 2 _2xI/3 2 _ 2xI/3-2 x3 x1 x1/3 xl/3…
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3.2 Rolle's Theorem Rolle's Theorem If f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b], and…
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11) f(x) = sin 2x, 0,2 "3 f is continuous on the closed interval [ ; 3 f '(x) = 2 cos 2x f is differentiable on the open interval |0, 3 .…
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The Mean Value Theorem If f is continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a…