Use the figure below to identify the following information, if it exists. If it does not exist, write does not exist.
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1
The relative minimum(s) is/are
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1
The absolute minimum value is
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The function is decreasing on
A particle moves along the x-axis. The function v(t) gives the particle’s velocity at time t > 0.
A. What is the particle's velocity v(t) at t = 4
B. Find the particle’s acceleration a(t) at t = 4
C. Att = 4,is the particle speeding up, slowing down, or neither? Justify.
The amount 𝐴(𝑡) of widgets produced by a manufacturer is given by the function
where 𝑡 is the number of hours of production since the start of the day at 7:00 am. At what time(s) is the rate of production the greatest?
Find the following. Use L’Hospital’s Rule when possible.
Find the limit, use L'Hospital's Rule, if necessary
A manufacturer has a monthly fixed cost of $175,000 and a production cost of $20 for each unit produced. The product sells for $32 per unit.
What is the cost function, C(x) ?
What is the revenue function, R(x)?
Compute the profit (loss) for a production level of 20,000 units. Interpret your findings.
P(x)=
Interpret :
Find the critical Numbers of f(x)
Find the open intervals on which the function is increasing or decreasing.
Increasing
Decreasing
*If something is not applicable, write N/A
Locate extremes.
Relative Max
Relative Min
Use the figure below to identify the following information, if it exists. If it does not exist, write does not exist.
The relative minimum(s) is/are
The absolute minimum value is
The function is decreasing on
A dog breeder has 40 feet of fencing to use for a rectangular dog run. If she puts the run next to the garage, she only needs to use the wire for three sides. What dimensions will yield maximum area?
Sketch the graph of a single function that has all of the properties listed.
Continuous and differentiable for all real numbers
Johny responded to the above information and has created the following cheat sheet to sketch the graph. Can you confirm his findings are True or False?
Use the graph below to evaluate the following:
Use the properties of integrals to evaluate each of the following, given that:
Evaluate
Consider a particle moving along the x-axis where
A. Find the Velocity of the particle:
B. Find the acceleration of the particle:
C. On what interval(s) is the particle moving to the right?
D.Find the velocity of the particle when the acceleration is 0.
Find the value of the definite integrals by using the Evaluation Theorem
Use the limit below:
Find the value of the definite integral.
What is the profit function, P(x)?
How many units should the company produce in order to make a profit of $50,000?