The rate of change in data entry speed of the average student is ds/dx = 4(x + 1)¬1/2, where x is the number of lessons the student has had and s is in entries per minute. (a) Find the data entry speed as a function of the number of lessons if the average student can complete 8 entries per minute with no lessons (x = 0). s(x) = (b) How many entries per minute can the average student complete after 35 lessons? entries per minute

Q: Find the 1st and 2nd derivative of this function: x=(t-2)5/2  y=t3-5

A: We will differentiate the function twice to get the first and second derivatives as follows while…

Q: Suppose that the revenue, in dollars, from the sale of x items was R(x) = 60x−0.5x^(2), and the…

A:

Q: 2) The amount of money (in billions of U.S. dollars) that a country spends on research and…

A: Here the amount of money that a country spend on research and development is given as a function. We…

Q: Find the absolute extrema of the function f(x) = (x + 16) 1/3 on the interval[-5,2]. Find the second…

A: To find  The absolute extremum of the given function.

Q: 8) A company's demand equation is x - V 2000 - p² , where p is the price in dollars. Find dp/dx when…

A:

Q: f(x)=x2+2 find average rate of change from -2 to 0 feom 1-3 and from -1 to 2

A:

Q: Use this formula to find the instantaneous rate of change of the function at the given x-value.f(x)…

A: Given function is

Q: 2х + 1 f(x) : х+ 2

A: Given:…

Q: Solve for the 2"nd derivative of the function f (x) = 3x5 – 4x3 + 7x² – 10. a. 15x* – 12x2 + 14x b.…

A: Given: fx=3x5-4x3+7x2-10 To Find: 2nd derivative of the given function

Q: 2. Given: y = f (x) = (2x-2 + 5x³). What is the slope (gradient) of the first derivative function at…

A:

Q: The marginal cost of serving a typical additional client at a law firm can be modeled by dC 675…

A: Given Data The equation of the marginal cost is dC//dx=675-0.5x.   Integrate the equation of…

Q: Find the first Derivative complete solution. r= (3cot42θ-4)2/3

A:

Q: The function f(x) = x2 describes the area of a square, f(x), in square inches, whose sides each…

A: Given function fx=x2 To find rate of change of area.

Q: Estimate the instantaneous rate of change of f(x)=3x²+2x−1_at x = -1. a) ΔΕ Δε O b) ΔΕ Δε Ο c) Δε Δε…

A:

Q: The function f(x) = x2 describes the area of a square, f(x), in square inches, whose sides each…

A: Given function fx=x2 to find rate of change of area.

Q: Find the rate of change of the function f (x) = (x + 1)/(1 - 5x) with respect to x when x = 1.

A: The given function f(x) - f(x) = x+11-5xRate of change of function is given by ddxf(x) =…

Q: The function f(x) = ᴫx2 describes the area of a circle, f(x), in square inches, whose radius…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: The rate at which the risk of Down syndrome is changing is approximated by the function r(x) =…

A:

Q: 10. Find a function y = ax +bx+c whose graph has an x-intercept of 1, a y-intercept of -2, and a…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the derivative of the function.

A: hs=-25s2+3

Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

A: Given that, the cost to produce x units per month is given by                C = 0.3x2+8,000  and…

Q: A company finds that the rate at which the quantity of a product that consumers demand changes with…

A:

Q: 2 For what values of x does the graph of f(x) = 2x° + 3x – 180x – 1 have a horizontal tangent line?

A: First we find the derivative of f(x), the slope of f(x) for horizontal tangent is 0 and the…

Q: Find the derivative of the function f(x) = – 2x1 + 5x – 7. A. -2x + 5 C. -2x? + 5 E. None of these…

A:

Q: A linear model of the spread of an epidemic in a community of 1000 people is the equation: dx/dt =…

A: To find the number of people x(t) who have contracted the disease at the time oftime t.

Q: Find the derivative of the function. x3 y -1 -2x3+3x2 y's (x- 1)2 y'= 2x-3x2 (x-1)2 y'= 2x3+ 332 (x-…

A:

Q: Suppose that a company's monthly profit depends on the number of units sold that month according to…

A:

Q: Use differentials to approximate the change in profit corresponding to an increase in sales (or…

A:

Q: Solve for the derivative of y IMPLICITLY 22 + Væ3 + 2y= y²

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: At any time t, the rate of growth of the population / of deer in a state park is proportional to the…

A: Solution of given question is written in below steps.

Q: An accessories company finds that the cost, in dollars, of producing x belts is given by C(x) = 730…

A: The cost function is Cx=730+37x-0.062x2To find the rate at which average cost is changing when x…

Q: The derivative of y x²+1 is х2—1 =

A:

Q: A culture contains 2000 bacteria initially and doubles every 60 minutes. Assuming that the rate of…

A: To determine the counting function P(t) explicitly, under the given conditions

Q: The rate of U.S. per capita sales of bottled water for the period 2000-2010 can be approximated by…

A:

Q: The weekly cost C, in dollars, for a manufacturer to produce q automobile tires is given by C = 2100…

A: Rate of change of cost function is the derivative of cost function with respect to time .

Q: Find the derivative of the function m: f(x)= e^x^3+4

A: Topic = Derivative

Q: Find the average rate of change of f(x) = 9x2 – 8 on the interval [2, t]. Your answer will be an…

A:

Q: Find the rate of change of the function at a given value. 1. f(x) = 2x – 3, at x = 5 2. f(x) = x² –…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Suppose that f(x)=-7x2 + 8 (A) Find the slope of the line tangent to f(x) at x=2 (B) Find the…

A: To determine the following for the function f(x) = -7x2 + 8:Part a) Slope of tangent at x = 2.Part…

Q: Find the derivative of the function. h(s) = −2√(5s2 + 3)

A: the given function is: hs=-25s2+3 we have to find the derivative of the given function.

Q: The number of bacteria in a culture is given by the function n(t)=950e^0.35t where t is measured…

A: The number of bacteria in a culture is given by n(t) = 950e^{0.45t}e0.45t

Q: a) Find the derivative of the function: T+ V3x f (x): 3x-1

A: Since you have asked multiple questions in single request so we  will be answering only first…

Q: The Snowtree cricket behaves in a rather interesting way: The rate at which it chirps depends…

A: Let x= number of chirps  y= temperature So two coordinates are (140,80) and (120,75)

Q: The rate of growth of a fish population was modeled by the equation G(t) =…

A: Consider the given: Gt=90000e−0.6t1+5e−0.6t2

Q: A culture contains 2000 bacteria initially and doubles every 40 minutes. Assuming that the rate of…

A:

Q: 1. What is the average rate of change of the function f(x) = x² - 4x + 7 on the interval 1 ≤ x ≤ 3?

A: average rate fo change in an interval (a,b) =f(b)-f(a)b-a

Q: Q2: A) Find an equation of the line tangent to the function of x² + (y-x)2 9 at x 1. dy x-x3 B)…

A:

Q: A manufacturer of handcrafted wine racks has determined that the cost to produce x units per month…

A:

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.