Q: Let y = 2 ln x - 1/2x then the first derivative is....., the first order condition is..... and the…
A: Given: y=2 ln x-12x To Find: To determine the first order derivative.To determine the first order…
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A: Second derivative is given by f''(x) = x(x+1)(x-2)2
Q: Find the second derivative. f(x) = 7e−x − 8e−7x f ''(x) =
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Q: 2. Find the root of the function using Fixed-point Iteration. f (x) = x cos (x) - x?
A: Consider the given function as, fx=xcosx-x2
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A: Find the first derivative. y=(x+1)(x+2)(x-1)(x-2)
Q: 10) Using the First Derivative Test, what are the local extrema for the function 5(x)==x²+10 x³…
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Q: 6. If f(x) = 3x2 . - x find f'(x), then find the equation of tangent line at r = 5.
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Q: 4)Given f(x) = 2x/(x2 + 1) a)Find the derivative. b)Find the critical numbers .
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Q: 10 Find the derivative f'(0) of f(x) = at x + 4 x = 0 using the laws of differentiation.
A: Derivative of the function
Q: first and second derivative of f(x)=x^2/(1+e^x)
A: To find first and second derivatives we will use product rule and quotient rule of derivatives. For…
Q: 2. Find all x values on the graph of f (x) where the tangent line is horizontal for each of the…
A: To find: The values of x on the graph f(x) where the tangent line is horizontal. Given information:…
Q: 3 + 3x – 5 Find the local maximum by solving the derivative P'(x)=0, – 2x + -- %3D |
A: Given Find out local maximum
Q: f(x)=ln(1+x/1-x) is function even or odd
A: We have to find the given function is either even or odd: fx=ln1+x1-x We know that for even function…
Q: Find the average rate of change of the function f(x) = x² - 2x + 3 between x = -2 and 2 = 4. Type an…
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Q: Find the equation of the tangent line to the function f(x) = ln(5x) at x = 8. (Use symbolic notation…
A: We have to find out the equation of tangent
Q: 3 ln x if x > 1 Determine if f(x) = is differentiable at x = 1. x² + 3 – 1, if x < 1
A: we have to check
Q: Find f(x) if f(2) - 2x 3 and the tangent line at x has slope (x – 1)e* %3D f(x) =
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Q: х+1 3.) y = х-2
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Q: Find the absolute maximum value of ƒ(x) = x2 ln (1/x) and say where it occurs.
A: We need to find the absolute maximum value of the function
Q: Domain of function f(x) = ln is (0, 2) O True False
A: Since you are asking multiple questions. We are answering only the first question. We have to check…
Q: poin Find the derivative with respect to x of f(x) = V2x + 6. f' (x) =
A: Given f(x)=2x+65
Q: The derivative of the function y = ecos²(x) is: y' = - sin(2x)eCos² (x) y' = sin(2x)eCos²(x) the…
A: We will find the derivatives of the given function y=ecos2x in the following step.
Q: 9.) f(x) = (2x + 1)* %3D
A: The integration technique to calculate the first derivative is:∫(ax+b)n-1…
Q: find the extreme values on the interval f (x) = x − 12 ln x, [5, 40]
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Q: f(x) = -3 sin(x) cos(x)
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Q: 3. Use the formula ((x+h)-f(x) to approximate the derivative of f(x) = 3x² at x = 1 h using h = 0.1.…
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Q: If F(x) is a differentiable function with derivative F'(x)= Enx"-1 and F(0)=0, then F n=2 x2-x O 1-x…
A: Introduction: For a differentiable function fx, if f'x is given, then integrating both sides, fx can…
Q: 3) Find the second derivative of 2x f(x) = for x + 0 3x2+4x Show all steps. Simplify your answer as…
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Q: 8.) f(x) = v5x* – 12
A: Given: fx=5x6-12 fx=5x6-1212 differentiating on both sides f'x=ddx5x6-1212
Q: 7 Find the derivative of f(x) 4/ + x4 Type your answer without fractional or negative exponents. Use…
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Q: A quadratic function f(x) = x + 3 x2 + 2 x + 3 has an inflectional tangent y = 3 x + 3 at (0,0).…
A: Given:- A quadratic function f(x) = x3+3x2+2x + 3 has an inflectional tangent y = 3x + 3 at (0, 0).…
Q: The second derivative of the function g is given by g' (x) = 0.1x³ – 0.29xª – 0.694x³ + 1.9136x². -…
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Q: 2.) f (x) %3D х
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Q: Find the inflection points of the function f(x) = x 2 ln x
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Q: 5. Find all x-values in which your function has horizontal tangent lines, f(x) = 2 sin x + x. given…
A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…
Q: Find the average rate of change of the function on the interval specified for real number h. f(x) =…
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Q: he tangent line to y= f(x) at (-7, -6) passes through the point (-9, -2). Compute the following. a)…
A: GIVEN DATA : Equation y=fx Tangent of the y=fx at -7,-6 passes through the…
Q: On the graph of f(x)=sinx and the interval [0,2π), for what value of x does the graph cross the…
A: Plot the graph of sinx given below
Q: 4. Given f (x) =x' -12x +1. Use the second derivative test to determine the local extremum of f (x…
A: See the attachment.
Q: 5) Use the tangent line at x = 9 to approximate the value of the function f(x)= Vx at x= 8.8.
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Q: Using Secant method, the approximation of the root of the function f(x) = xe*-x - 1 %3D accurate to…
A: The given function is f(x)=xex-x-1 And x0=0.7 & x1=0.76
Q: 5. Find the second derivative of f(x) = arctan(2x"). (You do not need to simplify your answer.)
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Q: 4. The derivative of f(x) = ln x at x = 3 when hpresent = 0.001 and hprevious = 0.002. %3D 5. The…
A: f(x)=ln…
Q: What is the derivative of f(x)=−3cos(x)+4sin(x) at the point x=π/3? Enter an exact answer.
A: Given, f(x)=−3cos(x)+4sin(x) We have to find the derivative of fx at x = π3
Q: 5 Let f(x) =x -e*. Find the value of x for which the second derivative f“equals zero. 2
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Q: 4. Using the expression (x + Ax)² = x" + nx-Ax +n(n – 1)x"-²Ax² + + Ax" ... prove that if f = ax"…
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Q: Q1. (1) The finite-divided difference approximations of the first derivative of the function f(x)…
A: The order of approximation deals with the Taylor series with a remainder. When the error is…
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- Determine dimension x to 3 decimal places.Find the linearization of ƒ(x) = sqrt(x + 1) + sin x at x = 0. How is it related to the individual linearizations of sqrt(x + 1) and sin x at x = 0?It works using the second derivative [ osxs] 1. Find the maximum and minimum limits of the function for the period | f (x)=x-4sin2x+2
- If (x, y) moves from (x0, y0) to a point (x0 + dx, y0 + dy) nearby, how can you estimate the resulting change in the value of a dif-ferentiable function ƒ(x, y)? Give an example.the value of x at which the FOC is satisfied give us the ........(maximum/minimum) of the function because the second derivative is ..........(positive/negative).Suppose that a nonnegativefunction y = ƒ(x) has a continuous first derivative on [a, b] . LetC be the boundary of the region in the xy-plane that is bounded below by the x-axis, above by the graph of ƒ, and on the sides by the lines x = a and x = b. Show that ∫ƒ(x) dx = - ∮C y dx.
- What is the average velocity of the curve y= square root of ( x2-2x) over the interval of [ 2,7]All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the surfacearea changing when each edge is 2 centimeters? Use the limit definition of a derivative to find f'(x) if f(x)= 1/(x-2). Find the equation of the tangent line to the graph of x + y - 1 = In(x^2 + y^2) at the point (1, 0).Find the exact location of all the relative and absolute extrema of the given function. f(x) = x − ln(x) with domain (0, +∞) The variable f has ---Select--- at (x, y) =