Solve the problem. 3t 7) Assume that the temperature of a person during an illness is given by T(t) = + 98.6, where T is the +1 temperature, in degrees Fahrenheit, at time t, in hours. Find the rate of Change of the temperature with respect to time. Find the intervals on which the function is continuous. Select the letter of the answer choice that BEST answers the question. 5 (x+5)2+ 10 A) No, since f(x) is not continuous at x = -5 B) Yes, f(x) is continuous at each real number C) No, since f(x) is a rational function D) Yes, since f(x) is continous at x = -5 3) Is the function given by f(x) = continuous on 5'? (all real numbers)? Use the Chain Rule to differentiate the function. You may need to apply the rule more than once. 9 ) f (x) = V/8x - (x2 - x+8)5 A ) f' ( x) = =(8x - (x2 - x+8) 5, 3/4 [8 - 5(x2 - x + 8)4] B) f' (x) = -(8x - (x2 -x+8)5 -3/4 [8 - 5(x2 - x + 8)+] C) f'(x) = =(8x - (x2 - x+8)5 -3/4 [8 - 5(x2 - x+ 8)#(2x - 1)] D) f' (x) = =(8x - (x2 - x+8)" 2 5, 3/4 [8 - 5(x2 - x+ 8)*(2x - 1)] E) None of these is correctProvide an appropriate response. 10) What is the derivative of a function f(x)? A) The derivative of the function f(x) is a function, usually denoted f'(x), whose output f'(a) is the instantaneous value of f(x) at the point (a, f(a)), where a is any value of x in the domain for f(x) where f'(x) exists. B) The derivative of the function f(x) is a function, usually denoted f'(x), whose output f'(a) is the average value of f(x) at the point (a, f(a)), where a is any value of x in the domain for f(x) where f'(x) exists. C) The derivative of the function f(x) is a function, usually denoted f'(x), whose output f'(a) is the average rate of change of f(x) at the point (a, f(a)), where a is any value of x in the domain for f(x) where f'(x) exists. D) The derivative of the fmetion f(x) is a function, usually denoted f'(x), whose output f'(a) is the instantaneous rate of change of f(x) at the point (a, f(a)), where a is any value of x in the domain for f(x) Where f'(x) exists. E) None of these is a valid explanation. Find the indicated derivative of the function. Assume there are no negative exponents allowed in the final answer. 4 11)dofy=3'\\jx d X Solve the problem. 14) Initially, a population of rabbits was found to contain 171 rabbits. It was estimated that the population was growing exponentially at the rate of 9% per day. Estimate the population after 48 days. 15) A business estimates that the salvage value V of a piece of machinery after t years is given by V(t) = menace-044*. After what amount of time will the salvage value be $698? Use the graph to determine the limit, if it exists. If it does not exist, explain why. Iim f(x) x~2+ 1) (1511.5 2 2.5 3 3.5 4 X