Find a formula for a function that has vertical asymptotes x = 6 and x = 8 and horizontal asymptote y = 6. f(x) :

Q: Given the function g(x) = 4x° + 12x² – 180x, find the first derivative, g'(x). = (x),6 Notice that…

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Q: For the function below, find a) the critical numbers; b) the open intervals where the function is…

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Q: On the graph of f(x) = sin x and the interval [-27, 0), for what value of x does f(x) achieve a…

A: First we draw a graph of sin(x) . Then we get at x=-π/2 sinx  achieve a minimum.

Q: Let h = ƒg be the product of two differentiable functions of x. a) If ƒ and g are positive, with…

A: We have given h = fg is product of two differential functions of x.

Q: Given the function g(x) = 8x° – 60x + 96x, find the first derivative, g'(x). g'(x) = Notice that…

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Q: For the function f(x) = x^4 / 1+x^3 answer the following questions, (c) Determine the open…

A: Given function is fx=x41+x3 Definition:- Let x=c is a critical of fx then If f'x>0 to the left of…

Q: Find the local and/or absolute maxima for the functions of the specified domain. Y= 1/(x-x^2) over…

A: Here we have to use the concept of derivatives. Here we use second derivatives test for finding…

Q: The graph of a function g is given. Estimate (9(x)dx with 6 equal subintervals using (a) right…

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Q: (c) F{-h(x+ 1) + 2h(x) – h(x – 1)}, where h(x) is the unit step function defined on page 235 of the…

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Q: find the points of inflection and discuss theconcavity of the graph of the function. y=x-\ln x

A: Consider: y=x-ln x. Find the inflection points and concavity of function. First find the domain of…

Q: For the function f(x) = -x-5x + 4x - 3, find: a. the critical values b. the intervals of increasing…

A: We have

Q: x'+1 Iff(x) = x² 2. What is the horizontal asymptotic of the function? Select one: OA1 O.B. 2 OC No…

A: To find  The horizontal asymptotes of f(x)

Q: (c) F{-h(x+ 1) + 2h(x) – h(x – 1)}, where h(x) is the unit step function defined on page 235 of the…

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Q: True or False The function f(x) = 2x/(x - 3) has y = 2 as a horizontal asymptote.

A: Given: fx=2xx-3 Concept Used: If degree of denominator is equal to the degree of numerator then…

Q: For the function below, find a) the critical numbers; b) the open intervals where the function is…

A: We need to find critical values and interval where function is increasing and decreasing.

Q: For the function f(x)=3cot*x determine its stretching factor and phase shift, and then graph it for…

A: fx=3 cotx Comparing with fx=Acotx, we get A=3 Now the stretching factor is, A=3 Phase shift is 0.

Q: Find constants a and b in the function f(x) = axeb" such that f(-) = 1 and the function has a local…

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Q: Use the graph of the function, f(x) =- X+8 to identify the function's horizontal asymptote. X+1'…

A: We will find the horizontal asymptote of the function as following.

Q: Example: Use the Secant method to estimate the root of f(x) = e-x-x. Start with initial estimates…

A: To use secant method to estimate the root of fx=e−x−x

Q: 12.x + 5x2 + 1 11. Determine the horizontal asymptotes of f(x): V16.x6 +6 1 12. Use the definition…

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Q: The local maxima occur at x The local minima occur at x = %3D

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Q: b) For f(x) = x* – 24x² + 11, find critical points, local and absolute extreme values, points of…

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Q: Given the function g(x) 6x – 27x2 – 72x, find the first derivative, g'(x). = (x),6 Notice that g'(x)…

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Q: Find the horizontal asymptotes of the function by computing the limits at infinity.

A: Givenf(u)=8u-316u2+6

Q: Sketch the graph of y = (x² – 1)² – (2x – 1)². [In your answer, you must include the following: •…

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Q: Given the following function: f(x) = x^2 lnx - Find the critical points for each of the functions…

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Q: For the function f(x)=6cotx determine its stretching factor and phase shift, and then graph it for…

A: Ans:  Given,  fx=6 cot x  We have to find the stretching factor and phase shift and   then graph it…

Q: For function, find (a) the critical numbers; (b) the open intervals where the function is…

A: Consider the function, y=x-4ln3x-9 Differentiate the given function with respect to “x” then,…

Q: 15. For this function find the coordinates of points on the graph that are local maximums or…

A: Local maxima and minima

Q: For the following exercise, find the critical points in the domain of the following function:…

A: giveny=sin2xdiffrentiatedydx=2sinxcosx=sin2xfor critical points putdydx=0

Q: Determine the equation of the function f(x) if it has a hole (point of discontinuity) at (6,3) and a…

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Q: shift

A: Given the function f(x)=4cotx To determine its stretching factor and phase shift, and then graph it…

Q: function

A: Second Derivative Test for Local Extrema:- The second derivative may be used to determine local…

Q: For the function below, find (a) the critical numbers; (b) the open intervals where the function is…

A: The solution of the problem is given in the next steps.

Q: identify the coordnates of any local maximum or minmum values of the function y=(x+3)2/ e2x

A: y=(x+3)2/ e2x Or, y = (x+3)2e-2x We need to find it's derivative and equate the same to zero.

Q: The function f is given by f (x) = (x² + 10x + 1)e¯". Find the critical (or stationary) points of f…

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Q: Given the function g(x) 6x + 63x² + 216x, find the first derivative, g'(x). = (x),6 Notice that…

A: We use second derivative test to determine the local Maxima and minima

Q: In an economic enterprise, the total amount T that is produced is a function of the amount n of a…

A: (a) The graph of the function is as follows: (b) Here, T(1.02)=-2(1.02)3+3(1.02)2+1.02…

Q: Given the function g(x) = 8x° + 84x² + 288x, find the first derivative, g’(x). = (x),6 Notice that…

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Q: The following graph of the derivative g' has exactly two roots.a. Find the critical points of g.b.…

A: a. The graph of g'x touches the x-axis at x=1 & x=2. That is, g'1=0  &  g'2=0 Therefore…

Q: The pressure of the oil in a reservoir tends to drop with time. By taking sample pressure readings…

A: Given that

Q: For the following function, find (a) the critical numbers, (b) the open intervals where the function…

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Q: Find the x value where the function g(x) = xe-lx attains a local maximum. Enter the exact answer. If…

A: Differentiate y and by solving y'=0 obtain critical points. Check sign of y'' on critical points -…

Q: Find a formula for a function that has vertical asymptotes x =1 and  x = 3and horizontal asymptote y…

A: Given that a function has vertical asymptotes x=1 and x=3 and horizontal asymptote is y=1. To find…

Q: 5x−12/x^2−x−42 has vertical asymptote(s) at x=

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Q: On the graph of f(x) = cos x and the interval [-27, 0), for what value of x does f(x) achieve a…

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Q: Sketch the graph of y = (x² – 2)² – x². [In your answer, you must include the following: • Find the…

A: We have to sketch the graph of function y=x2-22-x2

Q: Consider the function h(x) = ((x^2) - x) / ((x + 1)^2), which has first derivative h'(x) = (3x - 1)…

A: To find the vertical asymptotes, locate and classify all relative minima and maxima and point(s) of…

Q: Find the absolute maximum of h(x)=x2 −x−2 over [−3,6]. Enter only the y-coordinate of the maximum.

A: Determine the  derivative of the function  and find the critical points.