I need help! (Five Question)

1. [5 pts] Sketch a possible graph of a function that satisfies the given conditions. f(-1) = 3 lim f (x) = 1 x--1 lim f (x) = -1 x--1+ f is continuous but not differentiable at x = 2. There is a vertical asymptote at x = 1.2. [5 pts] In the early days of quantitative learning theory (around 1917), LL. Thurstone found that a given person successfully accomplished N (x) acts after x practice acts, as given by 1001: + 200 x + 32 Find the average rate of change of N(x) on the interval [8, 68]. Write a brief verbal N(x) = interpretation of this result based on the given problem. 3. [3 pts] The total profit (in dollars) from the sale of a: lawn mowers igiven by P(x) = 301: 0.03152 750 where O S x S 1000. Find the rate at which average profit per car seat is changing when 50 lawn mowers have been produced and sold. 4. [6 pts] The U5. consumption of copper (in thousands of metric tons) is given approximately by p(t) = 271:2 + 6,015, where t is time in years and t = 0 corresponds to 1990. a. Use the definition of the derivative to find p'(t). b. Find the U5. copper consumption in 2005. c. Find the rate of consumption in 2005. 5. [5 pts] Scott throws his math textbook vertically from the edge of a cliff and watches as it goes up and then falls into the ocean below. The height of the book above the water {in meters) is a function of time and is given by 110:) = 4.9t2 + 341: + 118, where gis in seconds. a. Find the velocity of the book after 5 seconds. Is the book rising or falling at this point? How do you know? b. Find the acceleration of the book at any time t. c. Find the velocity of the book when it hits the surface of the water