store finds that its sales Sales and advertising decline after the end of an advertising campaign. with its daily sales for the period declining at the rate S'(t) = -1477.8e-0.2t, 0

Q: Consider the two functions fz) = 5x +5 and g(x) = 5x² - 5. a. Determine the instantaneous rate of…

A: rate of change means differentiate with respect to x so differentiate it f'(x) = 10x g'(x) = 10x   a…

Q: The United States population (in millions) is predicted to be P(t) = 317e0.01t, where t is the…

A:

Q: Use second derivative method for the function y = 4x +21 x2+ 36 x - 20 to find i) the local extreme…

A:

Q: 3) Given the function g(x)= 2x² – 5x a) Find the derivative using the limit definition. b) Find the…

A: Since you have posted multiple subparts, as per our policy we will answer first question. Please…

Q: The tangent line to the graph of y = f(x) at the point (9, 20) has the equation y = 2x +2. (a) Find…

A: Use formula of instantaneous rate of change

Q: Determine the point(s) at which the graph of f(x) =  -4x/square root of 2x-1   has a horizontal…

A:

Q: Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and…

A: Given problem:- Sodium chlorate crystals are easy to grow in the shape of cubes by allowing a…

Q: e first derivative for the +1)(x +2) 2)

A: Find the first derivative. y=(x+1)(x+2)(x-1)(x-2)

Q: derivative k(t) = 4.8t3 − 4t2 + 2t − 9; t(x) = ln x

A:

Q: 34 - What is the value of the first derivative of the function at x = 2? A) 2 B) 1 C) -2/3…

A: Given y=ln[(x+1)/(x-1)] To find the first derivative at x=2

Q: a.) A sphere shaped balloon is being inflated with a rate of 800 cm³ per minute. When the radius of…

A:

Q: The relationship between a certain real estate company's quarterly profits, P(x), and the amount of…

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Q: Find an equation of the curve whose tangent line has a slope of f'(x) = 3x 10/11 given that the…

A: Given is derivative of f(x) we find f(x) so we integrate it.

Q: A box with a square base and open top must have a volume of 32000 cm³. We wish to find the…

A: Given that box has square box. side of square base is x.

Q: Calculate the derivative. y = x4 - 4 x² 5 (Give an exact answer. Use symbolic notation and fractions…

A:

Q: 2. Find the derivative y' for each function/curve. Once you solve for y', you do not need to…

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Q: According to Kleiber’s Law, the metabolic rate P (in kilocalories per day) and body mass mm (in…

A:

Q: Q:2. Use the first derivative test to find the intervals on which the function is f(x) = x4. which…

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Q: a. First compute the Derivative of f(x) = x and then use it to find the slope of the tangent line to…

A: Equation of Tangent to a curve: Let y=f(x) be the equation of a curve. Then the equation of tangent…

Q: A box with a square base and open top must have a volume of 296352 cm. We wish to find the…

A:

Q: 8) For the function y = x³ – 9x2 + 24x + 13, use the second derivative tests to: a) determine the…

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Q: The folowing is a reworded question from very last night . A printed solution of  a length of curve…

A: To find the correct integrand to evaluate the length

Q: The rate at which a cell absorbs an external signalling molecule x through the cell membrane can be…

A:

Q: For the drug metabolism function f(x) = -x(x+2)(x-3) , find the average rate of change of f(x) on…

A:

Q: Find the equation of the line tangent to the graph of f(x) = (In x)? at x= 8.

A: f(x)= (lnx)2

Q: dium chlorate crystals are easy to grow in the shape of cubes by allowing a solution of water and…

A: since it is given that, Sodium chlorate crystals are easy to grow in the shape of cubes by allowing…

Q: 8. Find the derivative of f(x) = -9/E + Type your answer without fractional or negative exponents.…

A:

Q: Find the average rate of change of f(x) = 3x - 4 on the interval 1, t|. Your answer will be an…

A:

Q: The amount, A, of anesthetics that a certain hospital uses each week is a function of the number, S,…

A: It is given that;  The amount, A, of anesthetics that a certain hospital uses each week is a…

Q: Q: Use the Second Derivative Test to classify the local extremes of the function f(x,y) =…

A:

Q: When observations begin at t=​0, a cell culture has 1100 cells and continues to grow according to…

A: Here a function is given which represents growth of the cells. We have to find the derivative of the…

Q: A box with a square base and open top must have a volume of 296352 cm³. We wish to find the…

A: It is provided that the base of the box is square and top of the box is open. The volumeV of the box…

Q: Solve the problem. Find the derivative of the function f(x y) = x² + xy + y² at the point (6, 7) in…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: You are lying on the beach watching a balloon float upward at a rate of 2 meters/sec from a point 50…

A: The balloon floats upwards at a rate of 2 meters/sec. The upward distance traveled after t seconds =…

Q: A basketball is thrown for a 3-point shot. The height of the basketball (in meters) is given by the…

A: To find the height from which the basketball is thrown, average velocity, instantaneous velocity and…

Q: Numerically estimate the slope of the line tangent to the graph of the function f at the given input…

A: Given f(x)=4x and x=2

Q: Use second derivative method for the function y= 4x' + 21 x²+ 36 x - 20 to find i) the local extreme…

A: The second derivative test is used to determine the points of local maxima and minima of a function.…

Q: 4) Suppose an object moves along a horizontal path with the position function x(f) = 4t – t2 on the…

A: Concept: Rate of change of position function at time (t०) gives velocity.  That is  Velocity…

Q: The population of a city grows from an initial size of 10,000 to a size P, given by P(t) =…

A: The given details are as follows. Pt=10000+50t2P0=10000 a. Obtain the growth rate as follows.…

Q: The tangent line to the graph of y=f(x) at the point (7,55) has the equation y=8x−1 (a) Find f′(7)…

A:

Q: f(x)= 16x2-4x+2; x=1 (a) Find the derivative, by using the definition (b) Find the instantaneous…

A: (A) Found the derivative using the definition. Answer: f'(x)=32x-4

Q: [4] For the Basic Absolute Value function f(x) = x, (a) state its slope (derivative) function (b)…

A: The absolute value function, |x| is defined as follows. |x|=xx≥0-xx<0   The graph of |x| can be…

Q: A ball is thrown upward with an initial velocity of 64 feet per second from an initial height of 80…

A:

Q: Can you please help me step by step with this problem?

A: We can see, that the graph of the function given is a straight line and the slope of the line is…

Q: 5. Find the second derivative of f(x) = arctan(2x"). (You do not need to simplify your answer.)

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Q: The functionf(x) is Find the first derivative in fa Set up a number line with t increasing,…

A: The given function is fx=3x5-5x4. Find the first derivative of the function by the power rule of…

Q: a. A spherical balloon is being filled with air at a constant rate of 2 cm³ per second. Write down…

A: We have to use formula for volume and surface are of a sphere in terms of radius (r) .  Volume…

Q: For the function f(x) = xe-2x give intervals of increase/decrease and intervals of concavity.…

A: Let's find.

Q: When observations begin at t= 0, a cell culture has 1800 cells and continues to grow according to…

A:

Q: Find the average rate of change of the function f(x) = = læ + 0x + 8, on the interval x E [-2,0].…

A: Given:fx=x2+8  on the    interval -2,0Average rate of change of the functionAx=fb-fab-aa=-2 , b=0

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.