Solve c part only 9. Consider the function y =with derivatives(a)Find any horizontal asymptotes of the function, or explain why none exist. Be sure to statewhether your horizontal asymptote(s) are on the right or left side.2(6-1)1D(b)Find the intervals where the curve is increasing and where it is decreasing. Also, find all z valuesor any local minimums or maximums values of the curve.Find the intervals where the curve is concave up and down. Also, find all z-values of anyon points, or state that there are none.

Concave Up , if the second derivative is positive . Concave down , if the second derivative is…

Answered: 9. Consider the function y = 22 with…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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11. Let h(x) = x^4 − 2x^2 + 3.(a) Find all critical points and use the First Derivative Test to characterize each as a local maximum, local minimum, or neither.(b) Use the Second Derivative Test to check your answers.(c) Find all inflection points.
Suppose that the first derivative of y = ƒ(x) is y' = 6(x + 1)(x - 2)2. At what points, if any, does the graph of ƒ have a local maximum, local minimum, or point of inflection?
The oxygen supply, S, in the blood depends on the hematocrit, H, the percentage of red blood cells in the blood. If S = k(H) = aHe-bH for positive constants a and b, with domain (0, infinity) and k'(H) = ae-bH(1-bH) 1. Use the definition to find the only critical point H1 of k on its domain. 2. Use a number line and the first derivative test to show that the oxygen supply is maximised at H1.You have to explain how you determine the sign of the first derivative on every interval. 3. What is the maximum oxygen supply? 4. How does increasing the value of the constants a and b in the same proportion change the maximumvalue of S? Please answer 3 and 4
1. A critical number of f′(x) is an inflection point of f(x).True or False 2. If the radius of a circle is increasing at a constant rate, then so is the circumference.True or False 3. If two variables x and y are functions of t and are related by the equationy = 1 −x^2, then dy/dt = −2x.True or False 4. When finding the global minimum of a function on an interval, you must usethe first or second derivative test to verify that your point is a global minimum.True or False
sketch the graph of y = x^3 / (x^2 - 4), keep in mind the information provided:1. x and y intercept: (0, 0)2. Vertical asymptotes: x = 2, x = -23. There is no horizontal asymptote.4. Discontinuity at x = -2 and x = 2.5. First derivative: y’ = (x^4 - 12x^2) / (x^2 - 4)^26. Critical points: x = 0, x = 2√3, x = -2√37. Intervals of increase: (-∞, -2√3) U (2√3, ∞)8. Intervals of decrease: (-2√3, -2) U (-2, 0)9. Local maxima: (-3.46, -5.20) and (3.46, 5.20)10. Second derivative: y’’ = (8x^3 + 96x) / (x^2 - 4)^311. Critical numbers: (0, 0), (√12, 3√3), (-√12, -3√3)12. Point of inflection: (0, 0)13. Concave upward: (-2, 0) U (2, ∞)14. Concave downward: (-∞, -2) U (0, 2) A sketch of the graph (by hand) - Labeling of vertical asymptotes on the sketch - Labeling of horizontal asymptotes on the sketch - Labeling of x and y intercepts on the sketch - Labeling of maximum and minimum points on the sketch - Labeling of points of inflection on the sketch A sketch of the graph on Desmos with all key…
a) On the number line, mark the critical value(s) of f(x) and the sign of the first derivative between them as obtained from the graph. b) Where is f(x) increasing on it's domain? c) Where is f(x) decresing on it's domain? e) At what x-value(s) would f(x) have a relative maximum? d) At what x-value(s) would f(x) have a relative minimum?
We want to study the following function on the interval I = [−2; + ∞[ g(x) = 3x2+4x+3/x2+1 a) Calculate its derivative and its critical points. b) Calculate the following limit: c) Determine the table of variations of g in I. Deduce whether there are relative minima or maxima, an absolute minimum and maximum in I.
The following graph of the derivative g' has exactly two roots.a. Find the critical points of g.b. For what values of x in (0, 3) is g increasing? Decreasing?c. For what values of x in (0, 3) does g have a local maximum?A local minimum?
Consider a function y =f(t) with domain (0. 1, 4. 2).Use the graph of the derivative function, y=f'(t) ,given below to write down the t -value of the local maximum of f. If the function has no local maximum, explain why not
Let f(x)=2x^2−5x+2 / 3x^2+11x+6This function has:1) A y-intercept at the point =2) x-intercepts at the point(s) =3) Vertical asymptotes at x = 4) Horizontal asymptote at y =
2. Suppose that f(x) is a function continuous for every value of x whose first derivative is f'(x) = 2(1-x)/1+x^2 and f"(x)= 4x(x^2-3)/ (1+x^2)^2 Further, assume that it is known that f has a horizontal asymptote at y = 0. and a. Determine all critical points of f.
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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