Calculus 101 Questions

1.

Trace or copy the graph of the given function f. (Assume that the axes have equal scales. ) Then use the method of this example to sketch the graph of f ' below it. C C CTrace or copy the graph of the given function f. (Assume that the axes have equal scales.) Then use the method of this example to sketch the graph off ' below it. y A rechargeable battery is plugged into a charger. The graph shows C(t), the percentage of full capacity that the battery reaches as a function of time t elapsed {in hours). C percentage of full charge 100 - 80 - 60' 20' t 2 4 6 8 10 12 (hours) (a) What is the meaning of the derivative C'(t)? C '(t) is the average rate of change of percentage of full capacity with respect to elapsed time in hours. C '(r) is the total percentage of full capacity with respect to elapsed time in hours. C '(t) is elapsed time in hours required for a given percentage of full capacity to be reached. C (It) is the instantaneous rate of change of percentage of full capacity with respect to e apsed time In hours. (b) Sketch the graph of C'{t). 100- 100 - 80- 80- 50- 50- 4D- 40' 20' 2.0- What does the graph of C'(t) tell you? The graph of C'(t) tells us that the rate of change of percentage of full capacity is decreasing and approaching 0. The graph of Cft) tells us that the rate of change of percentage of full capacity is increasing an approaching 100. The graph of C80) tells us that the rate of change of percentage of full capacity is increasing an without bound. The graph of CA\") tells us that the rate of change of percentage of full capacity is increasing an approaching 0. The graph of C' t) tells us that the rate of change of percentage of full capacity is decreasing wit out bound. Find the derivative of the function using the definition of derivative. g(x) = V4 - g' ( x ) = State the domain of the function. (Enter your answer using interval notation.) State the domain of its derivative. (Enter your answer using interval notation.)The graph of f is given. State the numbers at which f is not differentiable. X = (smaller value) X = (larger value) 2 XThe graph of f is given. State the numbers at which f is not differentiable. X= (smaller value) X = ( larger value) 0 2 4The graph of f is given. State the numbers at which f is not differentiable. X = ( smaller value) X= (larger value) 4 X