Concept explainers
If the total profit function for a product is
Is the marginal profit decreasing for all
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Mathematical Applications for the Management, Life, and Social Sciences
- Find the average rates of change of f(x)=x2+2x (a) from x1=3 to x2=2 and (b) from x1=2 to x2=0.arrow_forwardfind the value of x which gives the critical point.arrow_forwardIf the current production level is x items with cost C(x), then the cost of computing h additionial items is C(x+h). The average cost of those h items is (C(x+h)−C(x))/h . As we analyze the cost of just the last item produced, this can be made into a mathematical model by taking the limit as h→0, i.e. the derivative C′(x). Use this function in the model below for the Marginal Cost function MC(x).arrow_forward
- The marginal cost function for the manufacture of headphones is given by: where x is the number of headphones manufactured. Use a Riemann sum with n = 5 toestimate the cost of producing the first 5 headphones.arrow_forward1) Calculate the derivative of f1 (x) = (2x + 3) / (x - 5) using the definition of the limit of the rate of variation. 2) Calculate the derivatives of the following functionsarrow_forward1.) Find the area under the curve y = x3 + 3x2 and the axis between x = 1 and x = 3. 2.) Evaluate the first derivative of the implicit function: 4x2 + 2xy + y2 = 0arrow_forward
- Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning