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Consider the function f(x) = {2x3 - x2 +3x if x < 2, -36 +31x - 2x2 if x greater than or equal to 2}
a. Explain why f(x) is continuous and differentiable.
b. Graph the function in the xy plane where both x and y are non-negative. Find the positive values of x over which the function is increasing and decreasing.
c. Calculate the derivative of the function and explain why the sign of the derivative makes sense given your answers to part (b).
d. In your graph in (b), what value(s) of x minimize(s) the function for the domain and range given in (b)? Is df/dx=0 for these values of x? Why or why not?
e. Explain why x=2 is a point of inflection for f(x).
The method of maximum likelihood for estimating p states that we should choose the value for p that gives the highest probability of getting what we got on the experiment.
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write a rational expression for his average speed. 2) On Tuesday he drove for 6 hours at the same average speed. Write a rational expression for his distance on Tuesday.
A bullet is fired vertically upward. Its distance s (in ft) above the ground is given by: s=2250t-16.1t^2 where t is the time (in s).
Find the demand functions x∗(p, m) and y∗(p, m). Find the partial derivatives of the demand functions with respect to p and m, and check their signs. How does the optimal expenditure on the good x vary with p? (That is, compute the elasticity of px∗ ..
Similarly, one additional unit will be occupied for each 5 dollar decrease in rent. What rent should the manager charge to maximize revenue?
A sample of a radioactive substance decayed to 93% of its original amount after a year. (Round your answers to two decimal places).
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Compute the probability that the sampling plan will provide a result that suggests that SaveMor should reject the deal even if the true proportion of all customers who would switch is actually 0.70.
Determine, using the limit comparison test, whether the series with terms (n^4 + 3n)/(5n^3 + 9) converges or diverges. Which series did you use for the limit comparison test.
calculate the margin of error, E, for a 90% confidence interval for the proportion of all adults that watched the World Cup final on television.
An average computer mouse inspector can inspect 60 mice per hour. The 48 computer mice inspectors at a particular factory can only inspect 55 mice per hour with a standard deviation of 10. Does the company have reason to believe that these inspect..
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