f(x) = xln(2x) find the f '(0.5) as well as f''(1) and where is the absolute minimum located/ where does it occur?

Q: give a problem and solution for differentiation rule of exponential and logarithmic functions in…

A: The solution for the above question is as shown below.

Q: Find the relative extrema using both First and Second Partial Derivative test f(x) = Sin2x ; 0<x<n

A: i) The given function is fx=sin2x. Given that the domain of the function is 0,π. Obtain the first…

Q: Explain how the First Derivative Test determines whetherƒ(x) = x2 has a local maximum or local…

A: Given:   f(x) = x2 To determine whether f(x) has a local maximum or local minimum at the critical…

Q: 2. Show a graphical method of approximating the instantaneous rate of change at x = 3 for the…

A: You must have idea about what is the basic difference between instantaneous and average rate of…

Q: 4. Find an equation of the tangent line to the curve, f(x) definition of the derivative. (Don't use…

A: Given problem:- Find an equation of the tangent line to the curve, f(x) = 1/(x2 + 1) by using the…

Q: Estimate the instantaneous rate of change of P(x)=5/x+2 at the point x=2

A:

Q: 2. Determine the second derivative of f(x)= x'e* at x = -2 with a step-size of h=0.50 using Central…

A: Given function is f(x) = x2e2x and h = 0.50

Q: Estimate ln(0.9) using a linear approximation

A: Given:ln(0.9)

Q: Find the maximum or local minimum f(x)=sinx.[0,4]

A:

Q: 2. In y = 2" + x cosh 2x

A:

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: find derivative       1. y = ln 3x + x    2. y = ln (t2)    3. y = ln (3/ x)    4. y = ln (u + 1) -…

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

Q: The maximum value of y = cos x for - < x< is 1

A:

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: (b) Use implicit differentiation by partial derivative to solve for of function 3x2 + 2xy = -4y3. dx

A:

Q: To investigate these values, we find the second derivative f"(x) = %3D At the positive critical…

A: Given function is : fx=3x-4x3

Q: What is the connection of the concept of limits to slope to derivatives (delta method to simple…

A: The limits of the function at a point are calculated using the formula . The limits are used to…

Q: find x which minimizes the following function and its minimum with differentiation technique.…

A: We will find out the required solution.

Q: maximum point of y x – 2

A: Condition for Extreme Value: A continuous function fx, y has extrema at a, b if fx=fy=0 at a, b…

Q: A metal storage tank with fixed volume V0 = 360π m^3 is to be constructed in the shape of a right…

A: To find: The dimensions will require the least amount of metal. Given information: A metal storage…

Q: Give an example of a differentiable function ƒ whose first derivative is zero at some point c even…

A:

Q: The derivative of the function y = etan(4x) is: a) y' = tan (4x)etan(4x) b) y' = 4 sec²(4x) etan(4x)…

A: Given data: The given function is y=etan(4x). Differentiate the given expression with respect to x.…

Q: 2. Determine the second derivative of f(x) = x²e²* at x = -2 with a step-size of h=0.50 using…

A: Given function f(x)=x2e2x. The objective is to determine the second derivative of fx at x=-2 with a…

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

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: Given the first derivative is: y'=6x+1x-22

Q: (b) Use the First Derivative Test to identify all local extrema. Local minimum at x = Local maxiтит…

A:

Q: 4. Find an equation of the tangent line to the curve, f(x) = definition of the derivative. (Don't…

A: On solving this we will get

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: Please show me the partial derivatives for this homogenous equation and solve for GS/PS using Test…

A: Exact differential equation

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: (b) Use implicit differentiation by partial derivative to solve for dx of the function 5x + xy 4y.

A:

Q: Integrate xtanx with respect to x

A: We have to solve this integral by  Integration by parts rule, Formula is  ∫uvdx=u∫vdx-∫u'∫vdxdx

Q: 2. Use central difference approximations to estimate the first and second derivatives of y = e* at x…

A:

Q: find any locl maximum and locl minimum values by using first derivative: f(x)-x-2x

A: Given :           f(x) = x4 - 2x2

Q: Show that the function has partial derivative at the point (0,0) but is discontinuous at this point.

A: solve the following

Q: How do you find the partial derivative of a given function using the definition formula?

A:

Q: Find the linear approximation of the function f (x,y) = ln (x - 3y) at point (7,2).

A: To find the linear approximation of the function fx, y=lnx-3y at the point 7, 2.

Q: Find the length of the curve defined by 2 y = 5 ln 5 from x = 7 to x = 9.

A:

Q: Determine the second derivative of f(x) = x²e²x at x = -2 with a step-size of h=0.50 using Central…

A:

Q: Find the relative extrema using both First and Second Partial Derivative test f(x) = 1+8x - 3x2

A: i) The given function is fx=1+8x-3x2. Note that, the above polynomial function is real and defined…

Q: 2. Determine the second derivative of f (x)=xe* at x = -2 with a step-size of h=0.50 using Central…

A: Given f(x) = x2e2x

Q: The derivative of y=esinh/x + coshVx equals Select one: 1 1 (esinh/cosh/x + Vx² -1 2х 1 O y' = e…

A: We have to solve

Q: Find y(1) for y" = - 4z - 4y, X, = 0, yo = 0, z, = 1, with step length 0.1 using Euler method (2nd…

A:

Q: find any locl maximum and locl minimum values by using first derivative: f(x)=x*-2x?

A: The given function: f(x)=x4-2x2 To find the first derivative of the function: f'(x)=4x3-4x Now, let…

Q: 2. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the…

A: Product of two numbers:= 750; Sum of one and 10times the other is minimum;

Q: 4. Use the first and second derivative to find the absolute maximum and minimum, if either exists,…

A:

Q: A flexible stretched string is constrained to move with zero slope at one end x=0, while the other…

A: Given: A flexible stretched string is constrained to move with zero slope at one end x=0, while the…

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…