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Working with difference quotients Simplify the difference quotient
58. f(x) = 4x − 3
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Chapter 1 Solutions
Single Variable Calculus: Early Transcendentals Plus MyLab Math with Pearson eText -- Access Card Package (2nd Edition) (Briggs/Cochran/Gillett Calculus 2e)
Additional Math Textbook Solutions
Calculus & Its Applications (14th Edition)
University Calculus: Early Transcendentals (4th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
- Apply the properties of functions to correctly determine and interpret the break-even point in the following situations, using valid mathematical procedures and correct mathematical notation. Express your answer in terms of the context of the problem. The total monthly income of a nursery school for caring for x children is given by r = 500x, and its total monthly costs are c = 280x + 2500. How many children need to enroll monthly to break even? In other words, when do revenues equal costs?arrow_forwardThe average rate of change of a function f(x) = x2 between x = 4 and x = 9 is average rate of change = 9 − 4 = .arrow_forwardMr. dela Cruz encourages his students to solve math problems fast and with accuracy. He observed in his math class that the time it takes a student to solve x word problems is defined by the function f(x)= 3x2-x where f(x) is in minutes. Find the average rate of change in solving time from 3 to 5-word problems.arrow_forward
- Priya is comparing two functions: f(x) = 10 · x² and g(x) = 3 · 2* to find out which one has greater output values as x gets very large. She notices that f(1) = 10 and f(2) = 40. However, g(1) = 6 and g(2) = 12. She concludes that as x continues to grow, the values of f will be greater than the values of g . Explain or show why Priya's conclusion is incorrect.arrow_forwardMr. dela Cruz encourages his students to solve math problems fast and with accuracy. He observed in his math class that the time it takes a student to solve x word problems is defined by the function f 3x2- x where f(x) is in minutes. Find the averange rate of change in solving time from 1-3 word problemsarrow_forward11. Please explain how to get the domain, y-intercepts, zeros of the function, the x-intercepts, average rate of change from 0 to 3 of f(x)=2x^2+9x-5/4x^2+5x-6 (I don’t know If I started this right)arrow_forward
- A cube has an edge of 5 feet. The edge is increasing at the rate of 2 feet per minute. Express the volume of the cube as a function of m, the number of minutes elapsed. Assuming that the company sells all that it produces, what is the profit function? P(x)= I got at first 150m+125 but it is incorrect, please assist.arrow_forwardusing the definition of derivative to find f'(x) for the function:f(x)=4/x. How do I solve this?arrow_forwardConsider the following problem. A bicyclist is riding on a path modeled by the function f(x) = 0.05(8x – x2), where x and f(x) are measured in miles. Find the rate of change of elevation when x = 2. (Round your answer to two decimal places.) Decide whether the problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.arrow_forward
- Women in the Workforce Using data starting with 1950 and projected to 2050,the number of women (in millions) in the workforce is given by the function P=0.79x+20.86, Where x equals the number of years after 1950. (a)Find the Value of P when x=70 .Explain what it means. (b) What value of x represent 2030? Use the model to find the number of women in the worforce in 2020.arrow_forwardFind the point of diminishing returns for the function, where R is the revenue (in thousands of dollars) and x is the advertising cost (in thousands of dollars). Use a graphing utility to verify your results. R = −(1/4)x3 + 3x2 + 9, 0 ≤ x ≤ 6 (x, R) =arrow_forwardA travel agency will plan a group tour for groups of size 30 or larger. If the group contains exactly 30 people, the cost is $310 per person. If each person's cost is reduced by $10 for each additional person above the 30, then the revenue is given by the equation shown below, where x is the number of additional people above 30. R(x) = (30 + x)(310 − 10x) Find the marginal revenue if the group contains 35 people.$ Interpret your result. The revenue will increase by the absolute value of the marginal revenue in dollars if the group adds one person.The revenue will decrease by the absolute value of the marginal revenue in dollars if the group removes one person. The revenue will increase by $1 if the group adds the absolute value of the marginal revenue number of people.The revenue will decrease by $1 if the group adds the absolute value of the marginal revenue number of people.The revenue will decrease by the absolute value of the marginal revenue in dollars if the group adds one…arrow_forward