27. [0/3 Points] DETAILS PREVIOUS ANSWERS LARHSCALC2 2.AP.015. MY NOTES ASK YOUR TEACHER P Do not use technology. Consider the following table. X f(x) f' (x) g (x) g'(x ) 2 - 3 2 5 -2 5 4 8 -9 8 (a) If h(x) = f ( x ) find h'(2). g (x ) h' ( 2 ) = X (b) If j(x) = f(g(x) ), find j'(2). j'(2) = X ( c) If K( X ) . =.. . ( ( x ) , find k' (5). K'(5) = X Enter a fraction, integer, or exact decimal. Do not approximate. Need Help? Read It Submit AnswerC 8 G V V W Practice. G 41. [-/6 Points] DETAILS LARHSCALC2 3.AP.013. MY NOTES ASK YOUR TEACHER PRACTICE ANOT Do not use technology. The figure below shows the graph of f', the derivative of f, on the interval [-5, 4]. The function f is differentiable on the interval and f(-4) = 0. N -5 - -3-2 -2+ (a) Find f'(-2) and f"(-2). f' ( - 2 ) = f" ( - 2 ) = (b) At which x-values does f have a relative extrema on the interval (-5, 0)? (Enter your answers as a comma-separated list.) X = (c) Find all intervals on which the graph of f is concave downward. (Enter your answer using interval notation.) (d) Find the x-coordinate of each of the points of inflection of the graph of f. (Enter your answers as a comma-separated list.) X = (e) If g(x) = f(x) + sin'(x), is g increasing or decreasing at x = -7/4? increasing decreasing8 G 88 V V 48. [-/8 Points] W Practice.. DETAILS G C LARHSCALC2 4.AP.009. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER As a pot of coffee cools down, the temperature of the coffee is modeled by a differentiable function C, for 0 s t s 12, where time t is measured in minutes and the temperature C(t) is measured in degrees Celsius. Selected values of t are shown in the table. t (minutes) 0 3 5 8 12 C(t) (degrees Celsius) 64 55 47 42 40 35 (a) Evaluate "c'(t) dt. Indicate units of measure. ---Select--- Explain the meaning of your answer in the context of the problem. The value of / C'(t) at represents the ---Select--- from t = 0 to t = 12. (b) Explain the meaning of _ 12 Jo C(t) at in the context of the problem. The value of - 1 C(t) at represents the ---Select--- @ from t = 0 to t = 12. 12 Jo 1 / 12 C(t) dt. Indicate units of measure. (Round your answer to one decimal place.) Use a trapezoidal sum with 5 subintervals indicated by the table to approximate ---Select--- (c) Use the data in the table to approximate the rate, in C per minute, at which the temperature is changing at time t = 6. (Round your answer to one decimal place.) oC per minute (d) For 12 0. O F is increasing where f(x) > 0.38. [-/3 Points] DETAILS LARHSCALC2 3.AP.010. MY NOTES Do not use technology. ASK YOUR TEACHER Consider the function f(x) = 2x + cos(2x) on the interval [0, x]. (a) Find the maximum value of f. ( x, f ( x ) ) = (b) Explain how the conditions of the Mean Value Theorem are satisfied by f for 0 S x S n. Of is continuous on (1, ) and differentiable on (0, it). Of is continuous on [1, x] and differentiable on [1, m]. Of is continuous on (0, 7) and differentiable on (0, it). Of is continuous on (0, 7) and differentiable on [0, m]. Of is continuous on [0, x] and differentiable on (0, it). Find the value of x whose existence is guaranteed by the Mean Value Theorem. X = Need Help? Read ItG 28. [-/5 Points] B DETAILS LARHSCALC2 2.AP.016. G V V W Practice. MY NOTES Do not use technology. ASK YOUR TEACHER PRAC The figure below shows the graph of the velocity, in feet per second, for a particle moving along the line x = 4. V(1) (a) During which time interval(s) is the particle doing the following? Enter your answer using interval notation. (i) moving upward (0,1) U (ii) moving downward (iii) at rest (1,2) (b) What is the acceleration of the particle at the following times? (1) t = 0.23 it/$ 2 (ii) t = 4.8 ft / $ 2