Reference: Calculus and Its Applications, 12th, by Marvin L. Bittinger and David Ellenbogen Book

Elementary Applied Calculus

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List the points in the graph at which the function is not differentiable. Ay X XO X1 X2 X3 X4 X5 Select all that apply. B. X2 A. X4 OD. X1 OC. X5 F. XO DE. X3a. Use the Product Rule to find the derivative of the given function. b. Find the derivative by expanding the product first. f(x) = (x - 4)(x +5) a. Use the product rule to find the derivative of the function. Select the correct answer below and fill in the answer box(es) to complete your choice. O A. The derivative is (x - 4) ( ) + (x +5) (_) O B. The derivative is )x (1x + 5 ). O C. The derivative is () (x - 4). O D. The derivative is (x - 4)(x + 5) (_]) O E. The derivative is (x - 4)(1x + 5) + b. Expand the product. (x - 4)(x +5) = (Simplify your answer.) Using either approach, dy (x - 4)(x + 5) =\fDifferentiate the function y = 19 - 3x using the Chain Rule. dy dxGiven s(t) = 41" + 16t, where s(t) is in feet and t is in seconds, find each of the following. a) v(t) b) a(t) c) The velocity and acceleration when t = 2 sec a) v(t) = b) a(t) = c) When t= 2 sec, the velocity is (Simplify your answer.) When t= 2 sec, the acceleration is (Simplify your answer.)Find the exact value of the integral using formulas from geometry. W ( 3 + * ) dx W (3 + x)dx = (Simplify your answer.)Evaluate. (Be sure to check by differentiating!) 1(3+x 5 )8 5x# [(3+x5) 5x* dx= (Type an exact answer. Use parentheses to clearly denote the argument of each function.)Differentiate. Y=xex+20 -X+X 4 Choose the correct answer below. O A. dy =- 9xe - 9% 4-3X -20 -X -4x dx O B. dy = - 9x e - 9% 4 -9% -70 -X +4x dx O C. dy = - 9x e -9% _ - 9% - 2e -X +4x dx O D. dy =- 9xe -X+ 4x dxState the average rate of change for the situation. Be sure to include units. The population of Felton was 2300 in 2013 and 2600 in 2019. The population of Felton grew byFind an equation of the line tangent to the graph of f(x) = - 1- 9x" at (4, - 145). The equation of the tangent line to the graph of f(x) = - 1 - 9x" at (4, - 145) is y = (Type an expression using x as the variable.)Find the future value P of the amount Po invested for time period t at interest rate k, compounded continuously. Po = $400,000, t= 9 years, k = 3.7% P = S (Round to the nearest dollar as needed.)