calculus help please

1. [I1 Points] DETAILS MY NOTES | ASK YOUR TEACHEF 0f the two functions in gure below which is the derivative of the other? Y (j The blue function is the derivative of the red function. G The red function is the derivative of the blue function. 2. [13 Points] DETAILS Consider the three functions on the plot below. Which of the following are the graphs of f(x), g(x), and h(x) if f'(x) = g(x) and g'(x) = h(x)? 1. [-/4 Points] DETAILS MY NOT The graph below shows water level readings from a stream gauge as a function of time. Answer the questions below. Within the domain 0 w'(7) o w' (3) = w'(7) ow' ( 3 ) w'(5) ow'(0) V'(7 ) . V' (3 ) V'(5) From the choices below select the best graph of Vi(t). WARNING! This is worth three times as many points as a normal question and you get only one try. Think. Sketch your own graph of V'(t) first. Don't guess. MALIA dv/dt dv/dt3. [-/4 Points] DETAILS The function below shows the temperature of an object that is slowly thawing from frozen to room temperature. Answer the questions below Is degrees Celsius and ti -5 - Within the domain 0 s t T'(1) Which of the following is true? o T'(1) = T'(5) . T'(1) T'(5) From the choices below select the best graph of T'(t). WARNING! This is worth three times as many points as a normal question and you get only one try. Think. Sketch your own graph of T'(t) first. Don't guess. dT/dt drydt dT/dt dT/dt 24. [-/3 Points] DETAILS Height, h, is in cm and time, E, is in seconds. eight of an object bouncing on the end of an elastic band. 40 35 30 25 20 15 10 Sketch a graph ofh'(t). As usual, you should look for times when the velocity is zero. Also locate and compare different positive and negative velocities. Then select the t match from the choices below. WARNING! This is worth three times as many points as a normal question and you get only one try. dh/dt dh/dt dh/dt dh/dt5. [-/2 Points] DETAILS The graph below shows the electric potential in a circuit as a function of time. Use this graph and/or your graph of V'(t) from earlier in this assignment to answer the questions below. 20 V 15 10 -5 -10- - 15 -20- Within the domain 0 w'(7 ) o w'(3 ) = w'(7) ow' ( 3 ) w'(5) ow'(0 ) V'(7) . V'(3) V'(5) From the choices below select the best graph of V'(t). WARNING! This is worth three times as many points as a normal question and you get only one try. Think. Sketch your own graph of V'(t) first. Don't guess. dv/dt AA3. [-/4 Points] DETAILS the function below shows the temperature of an object that is slowly thawing from frozen to room temperature. The o Answer the questions below: IS in degrees Celsius and time, ; is Within the domain 0 T'(1) Which of the following is true? . T'(1) = T'(5) o T'(1) T'(5) From the choices below select the best graph of T'(t). WARNING! This is worth three times as many points as a normal question and you get only one try. Think. Sketch your own graph of T'(t) first. Don't guess dT/dt dT/dt dT/dt dT/dt4. [-/3 Points] DETAILS The graph below shows the height of an object bouncing on the end of an elastic band. 30 25 20 15 - Sketch a graph ofh'(t). As usual, you should look for times when the velocity is zero. Then select and compare different positive and negative velocities. WARNING! This is worth three times as many points as a normal question and you get only one try. dh/dt dh/dt dh/dt dh/dt5. [-/2 Points] DETAILS he electric potential in a circuit as a function of time. Potential, V, is in volts and time, t, is in seconds. Use this graph and/or your graph of V'(t) from earlier in this assignment to answer the questions below. 20 15 10 -10- -15- -20- Within the domain 0 s t s 7, when does the maximum (largest positive) rate of change occur? Select all that apply. ot = 0 sec ot = 1 sec of = 2 sec of = 3 sec ot = 4 sec of = 5 sec ot = 6 sec ot = 7 sec . The maximum rate of change occurs at times not listed above. o There is no maximum rate of change in the domain. Within the domain 0 s t s 7, when does the minimum (most negative) rate of change occur? Select all that apply. ot = 0 sec ot = 1 sec of = 2 sec of = 3 sec ot = 4 sec ot = 5 sec of = 6 sec ot = 7 sec The minimum rate of change occurs at times not listed above. o There is no minimum rate of change in the domain.6. [-/12 Points] DETAILS An object attached to a spring is moving back and forth Position, x, is measured in cm and time, t is measured in sec a fixed reference point, is a function of time as shown in the table below. t (sec) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 x (cm) | 0 11 14 15 14 11 6 0 -6 -11 -14 -15 -14 -11 -6 Using methods from the first week of class, estimate the velocity at timet = 0.5 seconds. Tolerances are set so that you must make reasonable use of the data. Include correct units. x'(0.5) = Repeat this until you fill in the table ofx'values below. Tolerances are similar. Do not include units. The table header has them. t (sec) 1.0 1.5 2.0 2.5 3.0 3.5 4.0 x'(m/s) poo t (sec) 4.5 5.0 5.5 6.0 6.5 7.0 7.5 x'(cm/s) Locate the earliest time when the velocity of the object is zero. You only get three tries. You must include units. Locate a second time when the velocity of the object is zero. Only three tries. Include units. When does the minimum (most negative) velocity occur? Only three tries. Include units. What is the minimum velocity? Only three tries. Include units. 7. [-/7 Points] DETAILS An object is cooling off. Its temperature in kelvins (K) is measured at 5 minute intervals as shown below. t (min) 0 5 10 15 20 25 30 35 40 45 50 55 60 T (K) 260.0 244.2 234.7 228.9 225.4 223.3 222.0 221.2 220.7 220.4 220.3 220.2 220.1 Compute the rate of change of temperature at all times in the table below. Do not include units. Be accurate to one decimal place. t (min) 5 10 15 20 25 30 35 40 dT (K/min) DOC Find an instant in time when the temperature is changing at a rate of -0.9 K/min (or cooling at a rate of 0.9K/min). You only get three tries. Include units. Find the temperature at the instant when it is cooling at a rate of 1.5 K/min. You only get three tries. Include units. How fast is the temperature changing at the instant the temperature is 222 K? Three tries. Include units.8. [-/4 Points] DETAILS MY NOTES ASK YOUR TEACHER An object is launched straight up. Its height as a function of time is given in the table below. t (s) 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 h (m) 5.00 5.65 6.20 6.66 7.02 7.28 7.44 7.50 7.46 7.33 7.10 6.77 6.34 5.82 5.20 4.48 Find an instant in time when the this problem, But note that you are limited to only three tries on each question, and you must include units. All answers must be accurate to one decimal place. Find an instant in time when the velocity is zero (or very close to zero). Find the velocity at the instant the height is 7.1 meters and the object is headed downward. Find the height at the instant when the velocity is -5.7 m/s