4. Determine the value of the constant k so that f(x) = e* (x + k) decreases on the intervals (- 0, - 3] and [0, 3].

Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: Given: fx=2x−1x2+3x2+1, and gx=x2+872−3x25 To check whether: f'x=4x2x2−1+2xx2+3−2xx2+12x2−1x2+3x2+1,…

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Q: 4.20 Consider the function f(x) = x' – 2x + 4 on the interval [-2, 2] with h = 0.25. Use the…

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Q: Suppose that the cost of producing x apple is c(x) = 2000 + 100x - 0.1x^2. Find the function f(x)…

A: We will find out the required function.

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A: Note: Since you have posted a question with two subparts, we will solve the first part for you.…

Q: 2. Compute the second derivative using forward, backward, central difference and Taylor for the…

A:

Q: 1. Find the derivative function for the following using the power rule: a) f(x) = x¹² b) y = 8x³ -…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: 4. Find the value(s) of x at which the graph of the function g(x)=x'e has a horizontal tangent line.

A:

Q: 11. Suppose a function is defined so that it has derivatives f'(x)=x²(1–x) and S"(x)=x(2-3x). Over…

A: Given that, the derivatives of a function f is defined asf'x=x21-xf''x=x2-3x We need to find the…

Q: Given the graph of derivative f'(x), find: a) Any interval(s) where f(x) is decreasing b) Any…

A:

Q: 2. Find the equation of the secant line on the curve f(x) = -x² +2 passing through the points ro =…

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

Q: Find a nonzero value for the constant k that makes the function tan(kx) f(x) = 3 3x + 2k2,…

A: Given: f(x)=tan(kx)x,   x<03x+2k2,   x≥0 A function f(x) is continuous at x=a, if limx→a-f(x) =…

Q: x-2 For the function 10x) = ind f(X), the third denvative of t and i ), the fourth derivative ofT…

A: Please refer the attached image for complete solution.

Q: 7. Suppose the equation əz ar is a differentiable function of r and y implicitly defined by 2³ = y²…

A:

Q: 4. Find the equation of the tangent line and the normal line to the graph of the given function at…

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Q: 1 4. Find the maximum value of f (x) = In(x- Inx) on the interval-<x<e. e

A: Given problem:- Find the maximum value of ƒ (x) = ln(x−lnx) on the interval 1/e≤x≤e

Q: 5 .Let f(x) =x² -e*. Find the value of x for which the second derivative s"»equals zero. 2

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Q: 1 Find the derivative of the following function: f(x) = e2X(3x² - vx) 2e2X(6x - 1/x) O e'(6x -…

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Q: Solve the initial value problems in Exercise for x as a functionof t.

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Q: (1) A course repeater claims that his brother who did some Calculus at college years ago, but…

A: for f'(x) see 2nd and 3rd step. for g'(x) see 4th and 5th step.

Q: 1) The derivative of f (x) = e2x² cos x is: 2) Simplifying the expression e n(4x-3) + eln 2x In(e3x)…

A:

Q: Q2:A/ Consider the function f(x) = 11x+3 -what are the first and second derivatives? -what are the…

A: We will answer the first three subparts of the first question as per our guideline. Please resubmit…

Q: True or False The graph of y = cos x is decreasing on the interval (0, π).

A: True or False The graph of y = cos x is decreasing on the interval (0, π).

Q: Find the indicated derivatives for #'s 1-6: 1. y'for y = 4In x 2. f'(x)for f(x) = In x³. 3. a. f'(x)…

A: As per guideline we have to solve three question

Q: 1. Find the linearization for f(x) = In(x) at x= e. (b) Use your linearization to approximate…

A:

Q: Let h be a function that has second derivative (x+ 1) (x – 2) (x + 4)e5 h"(x) Is x=2 the…

A:

Q: 2: The necessary condition for existence of the solution of the nonlinear equation x =g (x) in…

A: For any non linear function, to find the existence of its solution between an interval there should…

Q: (1) For every natural number n, x" = nx"-1 (you may use the product rule for derivatives and that x…

A:

Q: 2 Compute the derivative f'(x) of the logistic sigmoi 1 f (x) : 1+ exp(-x)

A: We have to find

Q: {fn(x)}1 converges a.e. to a function f(x) to be determined.

A:

Q: 19. Solve for A and B so that g(x) has a limit at both x = -1 and x = 3. 4x - 2, X> 3 g(x) Ax + Bx +…

A: To solve for A and B so that gx has a limit at both x=-1 and x=3. gx=4x-2,       x≥3Ax2+Bx+2,…

Q: Find the linearization L(x) ofy = e8# ln(x) at a = 1. L(x) =

A: We will use formula for linearization at one variable.

Q: 13.Find a sinusoidal function with a maximum value of 9 that occurs at x=4 , and a minimum value of…

A:

Q: find the absolute maximum and absolute minimum values of ƒ over the interval ƒ(x) = x - 2 ln x,…

A: The given function and the interval is,

Q: 2 2x +1 Let f(x) =- |- log, (x² + + 1) • (b* - 5b +3)x +c. If f(x)isa tan decreasing function of x…

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Q: Find the linearizationsof the following functions at x = 0. ln (1 + x)

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Q: 8. Find the derivative of the f(x) = ntan x at x = " А. п B. 2 In(1) C. π In (π) D. 2 n In() E. 2n…

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Q: 2. Given f(x) = x³ – 2x² + x + 2, find x e (-1, 3) such that f'(x) = 5. 3. Compute the derivative of…

A: Since you have posted multiple questions, as per our guidelines we are allowed to answer the first…

Q: 6. Suppose that the functions f and g and their first derivatives with respect to x have the…

A: a) fxg2x , x=1b) fx2+gx, x=0c) fx+gx, x=0

Q: 4. Find all derivatives of f(x) = x*, where k is some unknown natural number.

A: f(x) = xk and we need to find all the derivatives of f(x)

Q: 4. The graph of the first derivative f'(x) of a functionf is shown below. At what values of x does f…

A: Given graph of f'(x) is The value of x where f'(x)=0 are called as critical values where extrema…

Q: Based on a study, the Lorenz curves for the distribution of incomes for bankers and actuaries are…

A: Given: Lorenz curve for the distribution of incomes for bankers, fx=110x+910x3. Lorenz curve for…

Q: The equation of the tangent line for the graph of F(x)= Ln (f+4)df at x=2 is O y-Ln(68)(x-2) O…

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Q: Show mathematically that MRS is increasing for U=1-ex +e2y and is diminishing for U=lnX +LnY

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Q: 2. The Lorenz curve of a particular society is given by L(x) = Ax? + Bx. %3D Suppose that the…

A: We will use given values in Lorenz curve and Gini index to create equations for A and B , Then solve…

Q: 2. Consider the function h(x)=8+(x+3)*x"3 . a. Find all critical numbers for the function h(x).

A:

Q: A. Give a piecewise-defined function f (x) with no extreme values. B. Find for x² – 4xy + y² = 7 by…

A: A). A piecewise function is: fx=2x≤1xx&gt;1 Graph for this piecewise function is: B. Given function…