Business Calculus

Q1

Use the four-step process to find f'(x) and then find f'(2), f'(4), and f'(6). f(x) = 104x +1 f'(x) =]Refer to the graph of y = f(x) = x" + x shown. a) Find the slope of the secant line joining ( - 4, f( - 4)) and ( - 1, f( - 1)). b) Find the slope of the secant line joining ( - 4, f( - 4)) and ( - 4 + h, f( - 4 + h)). c) Find the slope of the graph at ( - 4, f( - 4)). d) Find the equation of the tangent line to the graph at ( - 4, f( - 4)). 5 a) The slope is .(Type an integer or a simplified fraction.)Suppose an object moves along the y axis so that its location is y = f(x) = x"+ x at time x (y is in meters, x is in seconds). Find (A) The average velocity (the average rate of change of y with respect to x) for x changing from 5 to 9. (B) The average velocity for x changing from 5 to 5 + h. (C) The instantaneous velocity at x = 5 second. (A) The average velocity is m/sec.Given x} = x2 2x, (A) Find f'() (A) PM = D If an object moves along a line so that it is at y=f{x} = 5x2 4x at time x {in seconds}, nd the instantaneous velocity function V: x), and find the velocity at times 3: = 1, 3, and 5 seconds {3! is measured in feet). v =f'{x] = [D] itisec Discuss the validity of the following statement. If the statement is always the, explain why. If not, give a counterexample. h The average rate of change of a function ffrom x = a to x = a + h is less than the instantaneous rate of change at x = a + E. Choose the correct answer below. 0 A. The statement is true. The average rate of change over smaller and smaller time intervals approaches the instantaneous rate of change, which is always greater than the average rate of change. 0 B. The statement is false. For example, a car could drive at an average speed of 40 mph from x = a to x = a + h, but be driving 45 mph for an instant at h )