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- 4) what is the first and second derivative of the equation W=8z^2 e^z1) Calculate the problem in the image as an anti-derivative. Make sure to include all steps:If the average rate of change of q (x) in the period (5,7) is equal to 8 and y (5)*y (7) = 16 and f (x) = 1 / y (x), what is the average rate of change of the function f ( x) In the same period ?!
- Government economists in a certain country have determined that the demand equation for soybeans is given by p = f(x) = 56/(2x^2+1) where the unit price p is expressed in dollars per bushel and x, the quantity demanded per year, is measured in billions of bushels. The economists are forecasting a harvest of 1.5 billion bushels for the year, with a possible error of 10% in their forecast. Use differentials to approximate the corresponding error in the predicted price per bushel of soybeans. (Round your answer to one decimal place.)Obtain regression equation of Y on X and estimate Y when X=55 from the ff.Suppose the percent of males who enrolled in college within 12 months of high school graduation is given by y= -0.126x + 55.72 and the percent of females who enrolled in college within 12 months of high school graduation is given by y= 0.73x + 39.7, where x is the number of years after 1960. Use graphical methods to find the years after these models indicate that the percent of females equaled the percent of males.
- State the derivative rule for the exponential function ƒ(x) = bx.How does it differ from the derivative formula for ex?Suppose two students are memorizing the elements on a list according to the rate of change equation: dL/dt = 0.5(1-L). L represents the fraction of the list that is memorized at any time t. (a) If one of the students knows one-third of the list at time t = 0 and the other student knows none of the list, which student is learning most rapidly at this instant? Why? (b) What does the rate of change equation predict for someone who begins with the list completely memorized? Explain.can you explain the whole process, step-by-step? like in an essay type. how did they find the first and second derivatives?