7) Write an equation for a rational function with the given characteristics vertical asymptotes at x = 5 and x = -5, x-intercepts at (2, 0) and (-1, 0), y-intercept at (0, 4)

Q: We have determined that there are two points where the slope of the tangent line is equal to 0. One…

A: We have given the function f(x)= x/x2+36

Q: Let f(x)=x² -3x+5. Show that the average rate of change of f (with respect to x) on an arbitrary…

A: Average rate of change = (f(b)-f(a))/(b-a) Instantaneous rate of change =f'(a+b/2)

Q: A manufacturer finds that the revenue generated by selling x units of a certain commodity is given…

A:

Q: d) A function with no absolute extrema but with a local minimum of -5 at x = 4 and a local maximum…

A: Follow the procedure given below.

Q: Find any local maximum & local minimum  of f(x)=-0.4x3-0.6x2+3x-4 on the interval (-6,4)

A:

Q: Find the quadratic approximation to f(x) = /x + 3 near a = 1. Graph f, the quadratic approximation,…

A: fx=x+3

Q: The graph of f(x) = 5(x – 1)2 – 6 is a parabola that opens --Select--- , with its vertex at (x, y) =…

A: Given equation  f(x) =5x-12-6

Q: 4. Use the first derivative test to find the intervals of increase and decrease, and the relative…

A:

Q: 3. Use Desmos to graph a cubic polynomial function, f (x) of your choice and it's derivative, f'(x)…

A: we will solve the 2 subpart question for you.  If you want any specific question to be solved then…

Q: The purpose of this question is to do the preliminary work to make a well-labeled sketch of the…

A: The function f(x) has critical points at c if f'(c) is equal to 0 or undefines. The critical numbers…

Q: (a) Find all the critical points, extreme values, interval of concavity and the zeros of the…

A:

Q: Suppose f(x) = =°+ 3z + 1. In this problem, we will show that f has exactly one root (or zero) in…

A: (A)

Q: Make a sign diagram for the derivative of the rational function. 7x f(x) x2 !! 16 -Select- v…

A:

Q: The process by which we determine limits of rational functions appliesequally well to ratios…

A:

Q: The purpose of this question is to do the preliminary work to make a well-labeled sketch of the…

A:

Q: find the maximum and minimum values of the func- tion on the given interval y=2x2−4x+2,  [0,3

A: Given y=2x2-4x+2

Q: A rectangle is constructed under the graph of f(r) = 4x with one corner at (7, 0) and one corner on…

A: Consider the rectangle. The top left corner of the rectangle lies on the curve y=4x2. Thus, the…

Q: The equation for the maximum deflection as a function of x is given by: -0.67665x10x -0.26689x10x³…

A:

Q: 7. Differentiate f(x) = (3x + x)² in three ways. When you have completed all three parts, show that…

A: Given that, fx=3x+x2

Q: Find the derivative of the function by the limit process. f(x) = x² + x - 5 f'(x) =| 4x – 8

A:

Q: 1. X > VX + 4 3+x 2. > 8 x+1 3. 4X 2 2 X+2

A: Since you have asked multiple questions, we will solve the first three questions for you. If you…

Q: Approximate the root of the equation f(x) = x^3 - x - 1 using 10 iterations on Bisection Method with…

A:

Q: 1 Sketch a graph of the function f(x) = 3 sin 5- 4- -87T -7 -6I -5 -47T -37 -27 27T 37T 47T -2- -3…

A: the amplitude of the function is 3 the time period of the function is  2π1/4=8π

Q: 3) Find the interval where the graph of f(x)= -2x' +3x +36x-1 is concave upward or concave downward.…

A: The given function is fx=-2x3+3x2+36x-1. Using second derivative test, the concavity as well as the…

Q: Find the interpolating polynomial for the function f(x) = e through the points x = 0, 1, 2.…

A:

Q: O Fend an equalion of the tangont line to the graph-of y-x-4Vx at (1-3). O Find an equalion -of #he…

A: If the slope of a line and any point (x1,y1) on it is known then its equation is given by :…

Q: Given the function g(x)=8x3-12x2-288x, find the first derivative, g′(x). g′(x)= Notice that g′(x)=0…

A:

Q: there are many ways to change the equation x3-xlnx - 1 = 0 to the fixed point x =g (x); form one of…

A: Given: x3-x ln x-1=0  Interval (0,2)

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: The process by which we determine limits of rational functions appliesequally well to ratios…

A: Given that limx→∞ x2+1x+1. Compute the limit as follows.

Q: The absolute minimum value of  f(x) = (x3/3) - ( 5x2/2) - 6x  on [-1,3] is?

A: fx=x33-5x22-6x,   -1, 3 Differentiating with respect to x, we get f'x=133x2-522x-61=x2-5x-6 Now to…

Q: True or false: Polynomial functions of degree 2 or higher have graphs that contain only rounded…

A: Consider the given information as Polynomial functions of degree 2 or higher have graphs that…

Q: 1 The equations of the vertical asymptotes of the function with rule f (0) = are: 1+ cose

A:

Q: Derive a 2nd order accurate finite difference expression for the first derivative at point i-1,…

A:

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

A:

Q: Determine the equation of a rational function where its domain is {x e R} and has an absolute…

A: According to the given information, it is required to determine the equation of rational function…

Q: On the interval -2 < x < 1, the function is… •maximum •minimum •increasing •decreasing •constant

A: Given a graph of any function. To find whether the function is maximum, minimum , increasing ,…

Q: Consider the image attached of the graph of a function y = g(x) on the domain -8 <= x <= 8, which…

A: Label the points on the given graph as shown below.

Q: write cosh(4 ln x) as a rational function of x

A: To solve the given problem apply the following formula

Q: 6. Determine the x-value of the absolute minimum of f(x) = -2x4 + 4x³ - 1 on the closed interval…

A: Given:       fx=-2x4+4x3-1     f'x=ddx-2x4+4x3-1    f'x=-8x3+12x2

Q: Find a formula for a function that has vertical asymptotes x = 3 and x = 9 and horizontal asymptote…

A:

Q: Find the maximum and minimum values of the function y = V8 + x2 - 4x on the interval 3, 5|. (Use…

A:

Q: Find a formula for a function that has vertical asymptotes x = 6 and x = 8 and horizontal asymptote…

A:

Q: Sketch the graph of a differentiable function y f(x) through the point (-2,2) if f'(-2)=0 and…

A: Given: To sketch the graph of the differentiable function function y=f(x) through point (-2, 2) if…

Q: Can you help with this problem step by step?

A: (a)

Q: graph of f(x) = 4(x – 2)² – 7 is a parabola that opens --Select- v with its vertex at (x, y) = ( and…

A:

Q: Investigate the connections between key properties such as increasing/decreasing intervals, local…

A:

Q: Suppose f(x) = x* + 3x + 1. In this problem, we will show that f has exactly one root (or zero) in…

A: Given that

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: Make a sign diagram for the derivative of the rational function. 27 f(x) x2 4x ---Select---…

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.