Answer problem 26, 28, 30, 32, 34, and 36 as true or false

25. If f' (2) = 8'(2) = 8(2) 26. If f is differentiable and increasing and if dx = Ax > 0, then Ay > dy. 27. If the radius of a sphere is increasing at 3 feet per second, then its volume is increasing at 27 cubic feet per second. 28. If the radius of a circle is increasing at 4 feet per second, then its circumference is increasing at 87 feet per second. 29. Di+4(sin x) = D*(sin x) for every positive integer n. 30. Du+3(cos x) = - D*(sin x) for every positive integer n. tan x 31. lim x-0 3x 3 " 32. If s = 5t3 + 6t - 300 gives the position of an object on a horizontal coordinate line at time t, then that object is always moving to the right (the direction of increasing s). 33. If air is being pumped into a spherical rubber balloon at a constant rate of 3 cubic inches per second, then the radius will increase, but at a slower and slower rate. 34. If water is being pumped into a spherical tank of fixed ra- dius at a rate of 3 gallons per second, the height of the water in the tank will increase more and more rapidly as the tank nears being full. 35. If an error Ar is made in measuring the radius of a sphere the corresponding error in the calculated volume will be approx imately S . Ar, where S is the surface area of the sphere. 36. If y = x, then dy 2 0