WebExample: First and Second Derivatives For Company Profit. Let’s say that a company has a profit function given by f(x) = -2x 2 + 800x + 10,000, where x is the number of items … WebNov 16, 2024 · The second derivative at \(x = 1\) is positive and so we have a relative minimum here by the Second Derivative Test as we also saw in the first example. In the case of \(x = 0\) the second derivative is zero and so we can’t use the Second Derivative Test to classify this critical point.

calculus - Can a function exist whose first and second derivative …

WebTranscribed Image Text: The function f, its first derivative, and second derivative are shown below. f (x) = 14in (x) - 5x² f' (x): 14 - 10x² X (a) Find the critical point of f. (b) Evaluate f" at the critical point you obtained in (a). f" at the critical point is: = Concave -Select-- (c) What is the concavity of f at the critical point you ... WebIn calculus, the second derivative, or the second-order derivative, of a function f is the derivative of the derivative of f. Roughly speaking, the second derivative measures … photo wedding guest book ideas

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WebThe second derivative of MC is positive for all values of Q, therefore the MC function is convex, and is at a relative minimum when q is equal to 8. Example 3: Find the optimum points of the profit function and determine what level of production Q will maximize profit. Start by taking first and second derivatives: WebFigure 1. Both functions are increasing over the interval (a, b). At each point x, the derivative f(x) > 0. Both functions are decreasing over the interval (a, b). At each point x, … Webthe second derivative test can fail at some points, as noted above. If the second derivative test fails, then the first derivative test must be used to classify the point in … photo weshden