6x+1 Given f(x) = 4x²+6x+9' 2. Use limits to investigate and then write a/n equation(s) for any horizontal asymptote(s) of f(x).

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Q: 1. Sketch the graph of y = sinx,0 ≤ x ≤ 360°, and complete the table below Maximum: Minimum:…

A: This question is based on graph of y=sinx

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Q: For the function y= x² -8x +20 a. Determine the critical points  b. Use the sign test to classify…

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Q: Find the x-coordinates of the absolute extrema of f(x) = -x² + 7x on the interval [1, 7]. Absolute…

A: f(x)=-x2+7x differentiating both side f'(x)=-2x+7 now f'(x)=0 -2x+7=0 x=3.5 So x=1, 3.5, 7

Q: 3. Iff has a local maximum at x – 1, then what can you say about f'(1)? What if you also know that f…

A: Given: The function fx has a local maximum at x=1. First derivative test: Let f be differentiable…

Q: 1. Find the maximum and the minimum values of the function f(x)= 2x – tanx %3D in the interval 3' 3

A: Given: f(x)=2x-tanx Differentiate the function with respect to x. f'(x)=ddx(2x-tanx)=2-sec2x…

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

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Q: On the graph of f(x) = cos x and the interval [-2n, 0), for what value of x does f(x) achieve a…

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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: 10. At what value of 'x' does a local maximum of y= x^3 - 3x occur?

A: We will solve the following

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Q: (a) The sales of a book publication are expected to grow according to the function S= 300000(1-…

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Q: 4. For the function f(x) = x* + 6x³+ 12x² + 8x + 1 find the domain, any symmetry, and the first and…

A: Given that the function is fx=x4+6x3+12x2+8x+1. The function fx=x4+6x3+12x2+8x+1 has no undefined…

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

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

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Q: Find an equation of the tangent line at x = 2

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

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Q: find the tirst asymptote of y = Tan(sx) %3D

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Q: Find the relative extrema of f(x) = 9+30x – 3x? using both first and second derivative tests. f(x)…

A: A detailed solution is given below.

Q: Find the critical numbers of the function f(x) = 14x + |x|. In the answer boxes below, enter the…

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Q: Find all maxima and minima f(x)= 0.9x^2 -6x-1 on horizontal span of 0 to 10

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A: Maxima and minima: Let f(x)=e3x2+4 For maxima or minima we need to find those values where f'(x)=0.…

Q: On the graph of f(x)=sinx and the interval [−2π,0), for what value of x does f(x) achieve a minimum?

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

A: Given, f(x)=x4-2x2

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Q: Consider the function y = -x3 + 3x² – 2. a) Find the critical points. b) Use the 2nd Derivative Test…

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Q: Find the minimum and maximum of the function y = x' - 9x? + 17 on [1,9] by comparing values at the…

A: For maximum and minimum values check the values of the function at the critical and the endpoints.…

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…

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

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Q: 311. When you find the maximum for an optimization problem, why do you need to check the sign of the…

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Q: using the de fini tion of first derivativg find the SlOpe of tange nt line to the g raPhof the…

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Q: 1) You wish to minimize f(x)=10x1²-x2² If you use steepest descent starting at (1, 1), will you…

A: As per the question we are given an unconstrained optimization problem as : minimize : f(x) = 10x12…

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Q: 13. Given the function f (x) = 2xv1 – x2. Determine the - c. Y intercept d. Vertical Asymptote(s)…

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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: Find the Horizontal Asymptote(s) of f(x) = 1+

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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 all vertical asymptote(s) for f(x) = r answers using limits. = √√7-√√3-x |x +41 (x2)) ●

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