Problem 7. (1 point) For what value of the constant c is the function f defined below continuous on (-oo, oo)? f(y) = y -c ify E (-00, 6) cy + 2 ify E [6, 00) C =Problem 20. (1 point) Find all critical values for the function 2r f(r) = 772 + 6 and then list them (separated by commas) in the box below. List of critical numbers:Problem 22. (1 point) (A) Estimate the area under the graph of f(z) = 16-22 from & = 0 to x = 4 using 4 approximationg rectangles and right endpoints. Estimate = (B) Repeat part (A) using left endpoints. Estimate =] (C) Repeat part (A) using midpoints. Estimate = Note: You can earn partial credit on this problem. Problem 23. (1 point) Consider the integral J." ( 2+3) do (a) Find the Riemann sum for this integral using right endpoints and n = 4. (b) Find the Riemann sum for this same integral, using left endpoints and n = 4 Note: You can earn partial credit on this problem.Problem 21. (1 point) Suppose that 7 f(x) = 2 - 36 (A) List all critical numbers of f. If there are no critical numbers, enter 'NONE'. Critical numbers = (B) Use interval notation to indicate where f() is increasing. Note: Use 'Inf' for oo, '-Inf' for -oo, and use 'U' for the union symbol. Increasing: (C) Use interval notation to indicate where f() is decreasing. Decreasing: (D)List the x-coordinates of all local maxima of f. If there are no local maxima, enter 'NONE'. x values of local maxima = (E) List the x-coordinates of all local minima of f. If there are no local minima, enter 'NONE'. x values of local minima = (F) Use interval notation to indicate where f(x) is concave up. Concave up: (G) Use interval notation to indicate where f (x) is concave down. Concave down: (H) List the x values all inflection points of f. If there are no inflection points, enter 'NONE'. Inflection points = (1) List all horizontal asymptotes of f. If there are no horizontal asymptotes, enter 'NONE'. Horizontal asymptotes y = (J) List all vertical asymptotes of f. If there are no vertical asymptotes, enter 'NONE'. Vertical asymptotes x = (K) Use all of the preceding information to sketch a graph of f. When you're finished, enter a "1" in the box below. Graph Complete:Problem 16. (1 point) Use linear approximation, i.e. the tangent line, to approximate v64.1 as follows: Let f(a) = Va. The equation of the tangent line in slope-intercept form to f(x) at x - 64 can be written in the form y = mx + b where: m = 6 = 1 Using this, we find our approximation for v 64.1 is NOTE: For this last part, give your answer to at least 6 significant figures or use fractions to give the exact answer. Note: You can earn partial credit on this problem. Problem 17. (1 point) Find the derivative of the function g(x) = (4x2 + 4x + 3)et 9(x) = Problem 18. (1 point) If f (z) = (sin -1 (7x + 3) ), then f' (20 ) = Note: The inverse of sin(x) can be entered as arcsin(x) or asin(x)Problem 13. (1 point) Find the equation of the line that is tangent to the curve y = 3x cos x at the point (7, -3TT). The equation of this tangent line can be written in the form y = mx + b where m = and b Note: You can earn partial credit on this problem. Problem 14. (1 point) Use implicit differentiation to find the slope of the tangent line to the curve defined by 2xy + xy = 12 at the point (4, 1). The slope of the tangent line to the curve at the given point is Problem 15. (1 point) The radius of a spherical balloon is increasing at a rate of 2 centimeters per minute. How fast is the volume changing, in cubic centimeters per minute, when the radius is 12 centimeters? Note: The volume of a sphere is given by V = (4/3) Tr3 Rate of change of volume, in cubic centimeters per minute, =