3.) The estimated monthly profit realizable by the Cannon Precision Instruments Corporation for manufacturing and selling x units of its model M1 cameras is P(x) = -0.04x^2 + 240x - 10000 dollars. Determine how many cameras Cannon should produce per month to maximize its profits. 4.) In the graph to the right, x1 and x2 occur where the profit function (the red graph) and the cost function (the blue graph) intersect. Give a brief explanation what the points x1 and x2 represent to our profit function.
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Profit is given by the difference between revenue and cost. Let's denote the number of cameras produced per month as $x$. The revenue function is given by $R(x) = 100x$, and the cost function is given by $C(x) = 0.01x^2 + 10x + 1000$. Now, we can find the profit Show more…
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The estimated monthly profit realizable by the Cannon Precision Instruments Corporation for manufacturing and selling x units of its model M1 cameras is P(x) = -0.04x^2 + 240x - 10000 dollars. Determine how many cameras Cannon should produce per month to maximize its profits. In the graph to the right, x1 and x2 occur where the profit function (the red graph) and the cost function (the blue graph) intersect. Give a brief explanation what the points x1 and x2 represent to our profit function.
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Given f(x) = x^2/(x^2 + 3), f'(x) = 6x/(x^2 + 3)^2, and f''(x) = -8(x + 1)(x - 1)/(x^2 + 3)^3, answer parts (a) through (m). Write "none" where appropriate. (a) Domain of f : (b) intercepts : (c) Vertical asymptote(s) : (d) Horizontal asymptote(s) : (e) Interval(s) where f is increasing : (f) Interval(s) where f is decreasing : (g) Local Minimum at x = (h) Local Maximum at x = (i) Interval(s) where f is concave up : (j) Interval(s) where f is concave down : (k) x-coordinate(s) of inflection point(s) for f : (l) Sketch the graph of f, Label all asymptotes, local maximum and minimum points, and inflection points.
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