Compute the average rate of change fix) = % on the interval [4,6]. Average rate of change = ':\\ Compute the average rate of change f{x) = v/x on the interval [3.92,4]. Round your answer to four decimal places. Average rate of change = \\:\\ The weekly demand function for office chairs is given by p = d(x) = 400 4x? where x is the number of hundreds of chairs and p is in dollars. Find the average rate of change of the unit price as the quantity demandad goes from 300 chairs to 500 chairs. l:l dollars per one hundred chairs Let f(x) = 3x2 - 15x. (a) Simplify (8 + h) - f(8) h Algebraically simplify your answer until you have cancelled out the factor of h in the denominator. (b) Evaluate lim f(8 + h) - f(8) h-0 h If an answer does not exist, enter DNE. (c) Determine the equation of the line tangent to y = f(x) at x = 8. Y=Let f( x) = Vx. (a) Simplify (22 + h) - f(22) h Algebraically simplify your answer until you have cancelled out the factor of h in the denominator. (Hint: See Problem #9 on Assignment 2.2 for similar computations.) (b) Evaluate lim (22 + h) - f(22) h -0 h If an answer does not exist, enter DNE. (c) Determine the equation of the line tangent to y = f(x) at x = 22. V=X -3 -2 -1 1 2 Answer each of the following questions about f(x). You have one submission for each question. (a) Does lim f(x) exist? x-3 OYes ONo (b) Is f(x) continuous at x = 3? OYes ONo (c) Is f(x) differentiable at x = 3? OYes ONo (d) Does lim f(x) exist? x- 1 OYes ONo (e) Is f(x) continuous at x = 1? OYes ONo\fLet f{x) = 94/ x. Simplify each of the following expressions. fis+h)fA5)= - x f53+h) A5 _ . , = {Mzake sure to cancel out the factor of h in the denominator) X h Let f{x) = 3x% 15x. (a) simplify M";'c{ Algebraically simplify your answer until you have cancelled out the factor of h in the denominator. 3h+ 33 4 (b) Evaluate lim fis+h) - A8) h=0 h If an answer does not exist, enter DMNE. w (c} Determine the equation of the line tangent to y = fix) at x = 8. Let f(x) = 1 X (a) Simplify (3 + h) - f(3) h Algebraically simplify your answer until you have cancelled out the factor of h in the denominator. (Hint: See Problem #8 on Assignment 2.2 for similar computations.) (b) Evaluate lim f(3 + h) - f(3) h-0 h If an answer does not exist, enter DNE. (c) Determine the equation of the line tangent to y = f(x) at x = 3. y =Let f( x) = Vx. (a) Simplify (22 + h) - f(22) h Algebraically simplify your answer until you have cancelled out the factor of h in the denominator. (Hint: See Problem #9 on Assignment 2.2 for similar computations.) (b) Evaluate lim (22 + h) - f(22) h -0 h If an answer does not exist, enter DNE. (c) Determine the equation of the line tangent to y = f(x) at x = 22. V=