Suppose fis a function whose derivative is given by f'(x) = following statements are true? (x-1)(x-4)3 1+x4 Which of the %3D I. The slope of the tangent line to the curve y = f(x) at x = 2 is -8. II. f is increasing on the interval (1, 4). III. f has a local minimum at x = 4.

Q: 3 Find the slope of the tangent line to x/y +yVx = 10 at (1,8).

A: given: x3y + y3x= 10differentiate given equation with respect to xx3 ddxy + y ddx x3+ y3ddxx+ x ddx…

Q: 5. Show that the equation of the tangent to the curve y = Inx + kx at x = 1 always passes through…

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Q: Suppose that f(x) is differentiable for x > 0, y = 2x + 1 is the tangent line to the graph of f at x…

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Q: 4. Find the point(s) on the curve of y=,x+x+2for which the slope of the tangent line is zero. (5)

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Q: Q2 find the derivative of the following: 1) y = 2stn²(5x) ,2) y = Inx'n cosh 5x ,3) xsin¬14y = y…

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Q: he tangent line to y = f(1) at (-3,9) passes through the point (9,-3). Compute the following.

A: The slope of the line passing through the points, (x1,y1) and (x2,y2) is given by .

Q: 2. Find the equation of the tangent line to the curve y = In(x'-7) at (2,0).

A: Given :          y=lnx3-7

Q: 3. The derivative of /(x) = In x at x = 3 when hourrent = 0.001 and hprevious = 0.002

A: Given problem:- 3. The derivative of f(x) = In x at x = 3 when hcureent= 0.001 and hprevious = 0.002…

Q: 4. A. Use the tangent line to find a linear approximation to the function f (x) = Vx near x = 64.…

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Q: When the graph of the derivative is positive then the graph of the antiderivative will be…

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Q: find the derivative of y with respect to the appropriatevariable. y = (1 - θ) tanh-1 θ

A: Consider the following equation:

Q: Find the derivative of the following functions: 5. y = tanh 2x +coth 3x ans. y' = sech²2x – 2csch²3x…

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Q: 18- What is equation of the tangent line of ƒ(x)=x³- 2x² - 1 at the point x = 2 ? y=-2x+9 1903…

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

A: see 2nd step

Q: The graph at the right show a relative minimum at the point , but y' # 0. How could we use the…

A: The cusp points on the curve can be identified as follows: If the function f(x) has the first…

Q: The derivative of y= sech-(Inx)+e sinh- (3x) equals Select one: +3esinh (3x) cosh(3x) y' = xlnxv…

A: The derivative of y=sech-1(lnx)+esinh-1(3x) is to be calculated by chain rule. The derivative of…

Q: Consider the following information fz(x, y) = 2xy - 2r³ and f₁(x, y) = x² + y² – 6. Use the Second…

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Q: The fifth-order partial derivative ∂5ƒ/∂x2∂y3 is zero for each of thefollowing functions. To show…

A: The given function is f(x, y)=y2-ysinx-x4.

Q: I Find tee e avation of tangent line of fcx) = X+) at X=2 X-3

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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: The slope of the tangent line to the curve y = 4/x at the point (3, 4/3) is: Must be written in y =…

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Q: 6. Differentiate: a. f(x) In (In (3x)) b. Find equation of the tangent line to the graph of y-e³x.…

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Q: Economists have considered the output y of a manufacturing process as a function of the size of the…

A: The output of a manufacturing process as a function of the size of the labor is given as follows.…

Q: 1 at x= 4 by using the 2Vx Q2. Find the slope of the tangent line to the function f(x)= definition…

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Q: on the chain rule find the tangent line to graph y=(x+2/x+1)^2, at x=0

A: We have to find tangent line to y , first we will find  value of y at x=0.

Q: (6) Find the derivative where it exists (c) Where is flz) analytic ?

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Q: .2 Find the tangent line to y = x-x+2 at x=2.

A: Given - A function To find- Equation of tangent

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 y with respect to the appropriatevariable. y = (θ2 + 2θ) tanh-1 (θ + 1)

A: The given function is y=θ2+2θ tanh-1θ+1. Obtain the derivative as follows.

Q: The derivative of y= sech-1(x sechx)+e$inh (Inx) equals Select one: – x sechx tanhx+ sechx O y:…

A: Given

Q: 4. Find the tangent line to the function f(x) =;xVx² + 5 at the point (2,2).

A: Tangent line of a function:  Differentiate the equation of the curve Substitute the value into the…

Q: 2. Approximate the derivative of f(x) forward, backward, and central difference method and step size…

A: To obtain the derivative at the point x0,y0, the following methods can be used:- The forward…

Q: Use Richardson extrapolation to estimate the first derivative of Y = sin x at * = π/4 using step…

A: Given the function  y=sinx

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

A: solve the following

Q: If fex, yJ-o find dy /af partial derivative off dx

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Q: Use Richardson extrapolation to estimate the first derivative of y = cos x at x = π/ 4 using step…

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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: 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: The value of the second derivative of at its point of inflection is A less than zero B equal to zero…

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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: So far, you've examined the function y = In x and its derivative, y' = , for large values of x. Now,…

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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: Approximate the derivative of y=x² at x=1 by forming small changes

A: We have to find the derivative of the function y=x2 at x = 1 by forming the small changes.

Q: A curve y = f(x) defined for values of x > 0 goes through the point (1, 0) and is such that the…

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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: 3. Find the siope of the tangent line that crosses through the point (3, 7) along the 2 curve f(x)=x…

A: Given :f(x)=x2-x+1

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…