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Q: 2. What is the average rate of change of the function f (x) = x² – 3x over the interval [1,1.01]?
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Q: 22) The critical points of the function F(x,y) = x³ + 3xy + y3
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Q: (2) Find the derivative of the following: y = xsinx + x² y = (x² + 1)** + sin(x*)+ x* 2. 3. Iny = e'…
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Q: 3. The Critical Point of y = xe-*
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- 11.Show that if a11, a12, a21, and a22 are constants with a12 and a21 not both zero, and if the functions g1 and g2 are differentiable, then the initial value problem x′1=a11x1+a12x2+g1(t),x1(0)=x01x′2=a21x1+a22x2+g2(t),x2(0)=x02 can be transformed into an initial value problem for a single second-order equation. Can the same procedure be carried out if a11, …, a22 are functions of t?At time t = 0, there is one individual alive in a certain population. A pure birth process then unfolds as follows. The time until the first birth is exponentially distributed with parameter λ. After the first birth, there are two individuals alive. The time until the first gives birth again is exponential with parameter λ, and similarly for the second individual. Therefore, the time until the next birth is the minimum of two exponential (λ) variables, which is exponential with parameter 2λ. Similarly, once the second birth has occurred, there are three individuals alive, so the time until the next birth is an exponential rv with parameter 3λ, and so on (the memoryless property of the exponential distribution is being used here). Suppose the process is observed until the sixth birth has occurred and the successive birth times are 25.8, 42.0, 52.0, 55.8, 59.2, 63.3 (from which you should calculate the times between successive births). Derive the mle of λ. [Hint: the likelihood is a…Consider the following nonlinear optimization problem: max 4*x+2*log(3*y+1) s.t. 2*x+log(3*y+1)<=5 y>=0 Which of the following statements about this problem is true? These concepts are not revelant since this is a nonlinear optimization problem This optimization problem exhibits infeasibility This optimization problem exhibits unboundedness This optimization problem has only one feasible solution This optimization problem has more than one optimal solution
- 13. Find the minimum and maximum value of the function on the giveninterval.y = 2x 2 + 4x + 5 [-2, 2]Consider the following real-world problem: Suppose that the population of Memphis is 22,400, and 60% of the population are susceptible to contract a serious illness from a very contagious bacteria that was introduced as a form of biological warfare. The remaining people have no reaction to the bacteria. Assume the susceptible people are equally mixed throughout the population. On January 1, 2022 (time t=0), the number N(t) of people who had contracted the disease was 180 and was increasing at the rate of 39 per day. Assume that N’(t) is proportional to the product of the numbers of those who have caught the disease and of those who have not. Write the differential equation that models the physical situation and solve for the exact answer.In an effort to make the distribution of income more nearly equal, the government of a country passes a tax law that changes the Lorenz curve from y = 0.98x2.1for one year to y = 0.32x2 + 0.68x for the next year. Find the Gini coefficient of income for both years. (Round your answers to three decimal places.) after before
- For a certain function, f'(x) = 0 and f' (x) > 0 for -1 < x < 2. Which statement is not true? a) (2, f (2)) is a local maximum b) (2, f (2)) is a critical point c) 2, f (2)) is a local minimum d) (2, f (2)) Is a turning point1. Use the function h(x)= x + x^2 - x^3 to complete the problems given below. a). The function h(x) has two critical values A and B, with AProve that the straight line y=3-2x intersects the exponential curve y=e^x at a point whose x-coordinate belongs to the interval (0,1).