Suppose that a firm uses L as an input, and its production function changes with L and a parameter a. Thus its profit is given by * = pf(L, a) – wL, where f is differentiable and increasing in a, and where p, w > 0. Using Envelope Theo- rem, find the derivative of the firm's maximal profit with respect to a and determine the sign of the derivative.

Q: Find the derivative of the function by the limit process. f(x) = 1/(x − 1)

A: We use the limit definition of the derivative

Q: Show both the Newton and Leibniz notation for finding the derivative of y = f(x) = 4x5.

A:

Q: Find the derivative of the function by the limit process.

A: Given: fx=x2+x-3 To Find: The derivative of the given function by the limit process

Q: FIND THE DERIVATIVE BY THE LIMIT PROČESS OFF(x) = Vx+2.

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

Q: Suppose that antibiotics are injected into a patient to treat a sinus infection. The antibiotics…

A: The concentration is given as , Ct=e-αt-e-βtβ-α where α and β are constants with β > α > 0.

Q: Find the derivative of the function by the limit process.

A: Consider the given function fx=1x2   Derivative of any function fx using limit process is…

Q: ; Compute the derivative of the function: f (x) = (+ Inx)² а.

A:

Q: 2. Calculate the first derivative of f using the forward and backward difference approach in the…

A: The objective is to calculate the first derivative of f using the forward and backward difference…

Q: Find the derivative of the function by the limit process. f(x) = √(x + 4)

A: Given function is

Q: Is this calculus statement true or false: "We can determine that h(x) =x^4 has a minimum at x= 0…

A: Given function is  Then x=0 is critical point of h as h'(0)=0, but also h''(0) =0  Therefore,…

Q: Estimate the root very near x = 0.4 of 4(x*)" - 4(x²) + 1 = 0 using the Newton- Raphson Method with…

A: Consider a function:  fx=4xx4-4x2x+1      =4x4x-4x2x+1

Q: Use forward difference approximation to estimate the first derivative of the following equation.…

A: Given that, fx=-0.15x3-0.2x2-0.5x+2.25h=0.5We need to find the first derivative of the function at…

Q: Find the critical coordinates of f(x) = x³ – 3x² + 8x + 1. Then, distinguish the local maximum and…

A: Given function is  f(x) = 13x3-3x2+8x+1                 ....(1) Differentiate with respect to x , we…

Q: Give an example of a function f (x) that has one positive derivative on (−1,0) and a negative…

A:

Q: 2. Determine the true error and relative true error when approximating the derivative of f (x) = -x²…

A:

Q: Determine the derivative of the following functions using chain rule. 3 * 1. f (x) = (2x² – 2x + 1)…

A: 1.f(x)=(2x2-2x+1)3 2. f(x)=5x3-8x2+9x-6

Q: Find the derivative of the function by the limit process. f(x) = x2 − 5

A: Given function is By limit definition of the derivative

Q: find the derivative of y with respect to x, t, orθ, as appropriate.

A: On simplification, we get

Q: 3) Find the derivative of the function f(x)= x² –x+2 using the definition of the derivative (a…

A: Given:     To determine: Derivative of the function using the definition of the derivative.

Q: Why does the maximum and minimum points for y = f (x) occur among the minimum and maximum points for…

A:

Q: 1. Use forward, backward and central difference to estimate the first and second derivative of f (x)…

A: Given function is fx=coshx and x=2 Step size h=0.01 We have to estimate the first and second…

Q: Suppose that the first derivative of y = ƒ(x) is y'= 6x(x + 1)(x - 2). At what points, if any, does…

A: The derivative of the function y=f(x) is y'=6xx+1x-2. We have to find at what points, if any, does…

Q: Find the derivative of the function by the limit process.

A: Given: fx=x2-5 To Find: The derivative of the given function by the limit process

Q: Shows that if a function f(x) is continuous in interval [a,b] then most likely the derivative of…

A:

Q: Suppose the derivative of ƒ is ƒ'(x) = x - 3.a. Find the critical points of ƒ.b. On what intervals…

A: We have to find: a. critical points of fb. On what intervals is f increasing and on what intervals…

Q: Find the derivative of the function by the limit process. f(x) = vX +7

A: Given,          The function is fx=x+7.

Q: Find the derivative of the function by the limit process. f(x) = x2 + x − 3

A:

Q: Find the critical value of f (x) = vx² + x – x using the second derivative test. %3D

A:

Q: Approximate the derivative of f(x)-x3+4x2-10x+5=0 at x=3 using the forward, backward and central…

A:

Q: Compute central difference approximations for the first derivative of the function, y =[ elnx)2 , at…

A:

Q: Find the derivative of the function. InV y = In 6 - X %3D y' = %3D

A: Explanation of the answer is as follows

Q: Find the derivative of f(x)  =(a + 2x2) (x - x2) in twoways: by using the Product Rule and by…

A: We have given function  fx=a+2x2x-x2 At first we  will use product rule:…

Q: Find the derivative of the function by the limit process. f(x)=x2+x-1

A:

Q: Find the derivative of the following using General Rule. 7) y = vt3 8) f(x) = 6 + 5 1 9) y =-+ 2 x3…

A: We have to find derivative of Given function.

Q: Find the derivative of a composite function using the Chain Rule or General Power Rule.  1.) y=…

A:

Q: 3. Estimate the derivative using forward finite divided difference applying both truncated and more…

A: Given f(x)=12+xe2x To find the f'0.5 at h1=0.25 and h2=0.125 using forward finite divided difference…

Q: Find the particular antiderivative of the derivative f'(x) = 3 -+x that satisfies the condition f…

A: Follow the procedure given below.

Q: Suppose the derivative of the function y=f(x) is y’=(x—1)^2(x—2). At what points, if any, does the…

A:

Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

A: The given Revenue function R(x)=23x3-40x2-450x.  Task: To maximize this revenue function.

Q: Using the đết of derivative, fin rivative of f(x) = x² + 2x + 2.

A:

Q: Suppose that the first derivative of y = ƒ(x) is y′ = 6(x + 1)(x - 2)2. At what points, if any, does…

A: To determine if the function has any points of maxima, minima or inflection, use second derivative…

Q: Find a linearization at a suitably chosen integer near a at which the given function and its…

A: Given function, fx=e-x a=-0.1 Formula for the linearization at x=a is given by Lx=fa+f'ax-a

Q: 3 Find the derivative with gicapeet to X If f(0 = 0-7 The derivatie with reapeet to X If -7X is…

A:

Q: Suppose that the first derivative of y = ƒ(x) is y′ = 6x(x + 1)(x - 2). At what points, if any, does…

A: Here the first derivative of the given function is y’= 6 x (x+1) (x-2). If a function has zero…

Q: (In iny

A: To find the derivative of the given function- lny=lnxylny Here we will use the following formulas-…

Q: find a linearization at a suitably chosen integer neara at which the given function and its…

A: Given: fx=xx+1 We want to find a linearization at a suitably chosen integer near a at which the…

Q: 2.) Investigate the derivate of the function f(z)=Imz by using definiton of derivative.

A: The derivative of a function is represented as the change in variable with respect to change in…

Q: In x g(x) = 2

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.