A company's profit P (in dollars) from selling x units of product can be modeled by  P (x)=500x-(1/2)x^2 The sales are increasing at a rate of 20 units per day. Find the rate of change of the profit with respect to time (in days) when 400 units have been sold.

Q: Explain how the first derivative of a function determines where the function is increasing and…

A:

Q: 2. how does the knowledge of differentiability and continuity determine the derivative of functions?

A: A function is said to be differentiable if the derivative of a function exists at all points. The…

Q: Find the rate of change of 1/x with respect to x when x=2

A: f(x)=1xrate of change of 1/x with respect to x isdf(x)dxdf(x)dx=-1x2

Q: Can the average rate of change of an increasing function ever be negative?

A:

Q: How can you sometimes graph the derivative of a function when all you have is a table of the…

A: We can draw the graph of derivative of a function using the values given to us in table of of the…

Q: The length of a rectangle is increasing at the rate of 4 cm/sec, while the width is increasing at…

A:

Q: A Cepheid variable star is a star whose brightness alternately increases and decreases. The most…

A: Given that the brightness of the Delta Cephei at time t( in days) has been modelled by the function…

Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: The given function of production cost is To find average rate of change of total cost ,use formula

Q: A helicopter is rising vertically from the ground at a constant rate of 6 m/s. When it is 75 m off…

A: Let x be the vertical distance travelled by helicopter and y be the horizontal distance travelled by…

Q: A circle is inside a square.The radius of the circle is decreasing at a rate of 4 meters per minute…

A:

Q: A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the…

A:

Q: Estimate the average rate of change for the graph above from X=2 to x=3 

A: We have to estimate the average rate of change for the graph above from x=2 to x=3 

Q: Can the instantaneous rate of change be different than the average rate of change in the same…

A: We describe that the instantaneous rate of change be different than the average rate of change in…

Q: what is the growth rate of the cells after 6 hours has gone by

A:

Q: Estimate the average rate of change from x = 1 to x = 4. %3D

A: average rate of change of f(x) on a,b=f(b)-f(a)b-aHere a=1 ,  b=4From graph f(1) = 5 ,  f(4) = 4

Q: At a certain instant, the radius of a right circular cylinder is 6 inches and is increasing at the…

A: The volume of a right circular cylinder is given by V=πr2h where r is the radius of the circular…

Q: A farmer has a field infested with nematodes and wishes to reduce their numbers. She applies an…

A: N'(t)=-43te710 To find out the formula for N(t) we take integral…

Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: Given,         The total cost in dollars from the production of x printers is given by…

Q: Match the graph of the function with the graph of its derivative.

A:

Q: Explain in 200 words the relationship between the secant line, slope of the tangent line, derivative…

A: Given: secant line, slope of the tangent line, derivative of a function using the limit process,…

Q: A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.4 cm/min.…

A: Given: The rate at which the radius is decreasing is, drdt=-0.4 cm/min. To determine the rate at…

Q: How do you find the derivative of the sum of two functionsƒ + g?

A: we have to determine how to determine the derivative of the sum of two functions that is f+g.

Q: What is the derivative of the exponential function ex? How does the domain of the derivative compare…

A: To determine the derivative of the function ex and domain of the derivative.

Q: Sand is taken out from its container at the rate of 104 cm/min. By the same pace, the sand is then…

A: Given: Rate of flow of sand =dvdt=104 cm3/min radius =r drdt=2 cm/min Now the volume of a cone…

Q: Sand is taken out from its container at the rate of 104 cm/min. By the same pace, the sand is then…

A:

Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: Suppose total cost in dollar from the production of x printers is given byC(x) =…

Q: How to find the rate of change of y=x^2-3 over the interval (-2,0)

A:

Q: Explain the relationship between the slope and the derivative of ƒ(x) at x = a.

A: Given function is  fx at x=a

Q: The length of a rectangle is increasing at arate of 5 cm per second and its width is decreasing at…

A: Given :- The length of a rectangle is increasing at a rate of 5 cm per second and its width is…

Q: 3. Tak-gu baked 10 loaves of bread in 1 hour. After that, he baked a dozen of bread in 80 minutes…

A: We have three points,  A = (60 min, 10 )  B = (80 min, 12 )  C = (90 min, 12)    Hence, we have…

Q: A light is placed on the ground 12 meters from a building. A man 2 meters tall walks from the light…

A: We can solve the given problem by using the  differentiation rules. If y  is a function of x then…

Q: How to solve for the second derivative?

A: The objective is to solve for the second derivative. Consider a function fx=3x4

Q: Oil is leaking from a pipeline on the surface of a lake and forms an oil slick whose volume…

A:

Q: Find the rate Of Chaange the folloewing in Table de. X 1-2)-1 TO fex) F3 -1 3.

A: Given that table values, x -2 -1 0 1 f(x) -3 -1 1 3 Use the formula of the rate of change,…

Q: A particle is moving along the curve y=4sqrt(2x+3). As the particle passes through the point (3,12),…

A:

Q: The length of a rectangle is increasing at arate of 5 cm per second and its width is decreasing at a…

A:

Q: How do you find the derivative of the quotient of two functionsthat are differentiable at a point?

A: Given: Let f and g be two differentiable function at point x.

Q: average rate of change

A:

Q: It is known that a bacterial culture increases at a rate that is proportional to its current amount.…

A: Given- Number of bacterial fibers after 1 hour=1000 Number of bacterial fibers after 4 hour=3000

Q: Solve for the second derivative of the function below 3. у%3 (х— 5)*

A: Given: y = x-54 To find: Second derivative of the given function.

Q: A potter forms a piece of clay into a right circular cylinder. As she rolls it, the height h of the…

A: we know that volume of right crcular cylinderV=πr2hdifferentiate…

Q: How do you find the derivative of the product of two functionsthat are differentiable at a point?

A: Consider the two functions f(x) and g(x). f(x)·g(x)'=f'(x)g(x)+g'(x)f(x). Here f(x)·g(x)' represents…

Q: A circle is inside a square.The radius of the circle is increasing at a rate of 3 meters per minute…

A: First, find the area outside the circle but inside the squareLet ‘s’ be the side of the square and…

Q: Explain how the instantaneous rate of change of a function at a point is related to its average…

A: Instantaneous rate of change: The instantaneous rate of change is the change in the rate at a…

Q: What is the rate of change of the function

A:

Q: Let g(x)=7arctan(5x). What is the instantaneous rate of change of g(x) when x=2?

A: g(x)=7arctan(5x) to find rate differentiate g(x) with respect to x

Q: Suppose total cost in dollars from the production of x printers is given by C(x) = 0.0001x3 +…

A: Given,          The total cost in dollars from the production of x printers is given by…

Q: An emply container is filled with liquid. The height of the liquid in the container is x cm and its…

A:

Q: A Cepheid variable star is a star whose brightness alternately increases and decreases.The most…

A: The rate of change of a function f(t) is the first derivative of f(t) with respect to t.

Q: A hot object is placed in a room whose temperature is 69°F. After 1 minute the temperature of the…

A:

Exponential Growth Model

The relation that represents an exponential function is: