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4.4_Absolute_Extrema

4.4_Absolute_Extrema - 2 – 8 on-4,2 Find the absolute max...

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4.4 Absolute Extrema The Absolute Extrema of a function: If f(x) < f(c) for all x in the domain of f, then f(c) is called the absolute maximum of f If f(x) > f(c) for all x in the domain of f, then f(c) is called the absolute minimum of f THEOREM If a function f is continuous on a closed interval [a,b], then f has both an absolute maximum value and an absolute minimum value on [a,b]. Finding the Absolute Extrema of a function, f, on a closed interval Find the Critical Numbers of f that lie in (a,b). 2. Compute f(a) and f(b). (i.e. the y’s) 3. Compute the value of f at each critical number found in step 1. (i.e. the y’s) 4. The absolute maximum of f is the largest of the numbers found in steps 2 and 3. 5. The absolute minimum of f is the smallest of the numbers found in steps 2 and 3. Find the absolute max and absolute min of f(x) = x 3 + 3 x
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Unformatted text preview: 2 – 8 on [-4,2] Find the absolute max and absolute min of f(x) = 3x 4- 4 x 3 +4 on [-1,5] Find the absolute max and absolute min of f(x) = 7x 2 + 7 x – 5 If f(x) = 1/ (x 2 + 4), Then f’(x) =- 2x/( x 2 + 4) 2 . Find the absolute maximum Find the absolute minimum If f(x) = x/ (x 2 + 4) on [-1,4], , Then f’(x) = - (x-2)(x+2)/( x2 + 4) 2 . Find the absolute maximum Find the absolute minimum A watch company is marketing a new high-end watch. The demand function is given by p= 360 – (1/3)x for 0< x< 20, Where p is the price in dollars and x is the number of units sold at price p. The cost function for producing x units per day is C(x) = 100 + 216x. Therefore, the profit function is P(x) = 144x – (1/3)x 3 – 100. How many watches should be produced each day to maximize profit?...
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