(a) Graph the given function, (b) find all values of x where the function is discontinuous, and (c) find the limit from the left and the right at any values of x where the function is discontinuous. 2x + 3 if x 50 h(x) = x2 - 5x+3 ifx>0 (a) Choose the correct graph below. O O O O (b) Select the correct choice below and, if necessary, fill in the answer box within your choice. O A. The function is discontinuous at x = (Use a comma to separate answers as needed.) O B. The function is continuous for all values of x. (c) Find the limit or limits from the left and from the right for any values of x found in part (b). Select the correct choice below and, if necessary, fill in the answer boxes within your choice. O A. No discontinuities were found in part (b). O B. The limit(s) from the left is/are . The limit(s) from the right is/are (Use a comma to separate answers as needed.)\fSuppose that the total profit in hundreds of dollars from selling x items is given by P(x) = 2x- - 4x + 9. Complete parts a through d below. a. Find the average rate of change of profit as x changes from 4 to 6. sper item b. Find the average rate of change of profit as x changes from 4 to 5. per item c. Find and interpret the instantaneous rate of change of profit with respect to the number of items produced when x = 4. (This number is called the marginal profit at x = 4.) 5 per item What does this result mean? Choose the correct answer below. O A. When items are sold for $ the profit is increasing at the rate of $4 per item. O B. When 4 items are sold, the profit is decreasing at the rate of $ per item. O C. When items are sold for $ , the profit is decreasing at the rate of $4 per item. O D. When 4 items are sold, the profit is increasing at the rate of $ per item. d. Find the marginal profit at x = 6. s per itemUsing the definition of the derivative, find f'(x). Then find f'(1), f'(2), and f'(3) when the derivative exists. f(Xx) = - x~ +9x - 2 f'(0) = (Type an expression using x as the variable.) Select the correct answer below and, if necessary, fill in the answer box to complete your choice. O A. f (1)= (Type an integer or a simplified fraction.) O B. The derivative does not exist. Select the correct answer below and, if necessary, fill in the answer box to complete your choice. O A. f(2) = (Type an integer or a simplified fraction.) O B. The derivative does not exist. Select the correct answer below and, if necessary, fill in the answer box to complete your choice. O A. f(3)= (Type an integer or a simplified fraction.) O B. The derivative does not exist.Using the definition of the derivative. find f'(x). Then find f'(- 1). f'(0). and f (3) when the derivative exists. f(x) = 4x" + 8 f(x + h) - f(x) To find the derivative, complete the limit as h approaches 0 for h lim h-+0 Find f (x) using the definition of the derivative. f'(x) =] Find f'(- 1) if the derivative exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. F (- 1)= (Simplify your answer.) B. The derivative does not exist. Find f'(0) if the derivative exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. f (0)= (Simplify your answer.) O B. The derivative does not exist. Find f (3) if the derivative exists. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. f (3) = (Simplify your answer.) O B. The derivative does not exist.For the given function, find (a) the equation of the secant line through the points where x has the given values and (b) the equation of the tangent line when x has the first value. y = f(x) =x~ +x x= - 4, x= -2 a. Which of the following formulas can be used to find the slope of the secant line? -2-(-4) f( - 2) + f( - 4) O A. f(-2) - f( - 4) O B. -2+ (-4) f( - 2) - f( - 4) -2+(-4) OC. -2-(-4) OD. f( - 2) + f( - 4) The equation of the secant line is - 5x - 8 b. The equation of the tangent line at x = - 4 is y = -7x - 16