2. Find the domain of the following function. State your answer in interval notation. 2х- 1 + vx 2. g(x) = V20 + x – x²

Q: How can I explain what it means for a function f(x) to be O(1)?

A: The 'f(x) to be O(1)' is to be read as function f(x) is of the order of 1.  Now refer to step two to…

Q: B- Find the local extreme points of the function f(x, y) = 4xy - x - y^.

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Q: nd the points where the function f(x) = (x² – 1)³ is decreasing, -

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Q: For what values of x does the graph of f(x)=2x^3+15x^2−36x−5 have a horizontal tangent line?

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Q: Q1.Given: x? – 4 | when x 3 1.Find what values of ( a) and (b) that will make the function…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: (b) Determine the domains and range of this function: y = v1 -x-

A: The given function is y=1-x2 the domain of the function is -1≤x≤1 In the interval notation the…

Q: find the value of the constant ( a, b, or c) that makes the function continuous.

A:

Q: Determine the range of the following functions. Express your answers using interval notation y =…

A: The graph of y=3x2, -2≤x≤2 is shown below:

Q: Left f(x) = Vx² – 8 be a function defined on the interval [0, c). Find the solution to f(x) =0.…

A:

Q: 3) Let f (x) = e=x² Where is y'> 0? What does this tell you about the original function?

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Q: Describe how you could use the graph of f(x) = 2" to obtain a decimal approximation for V2.

A: y=2x

Q: Find the graph of the function f(x) = [x] + [x/2] from R to R.

A: Given function is fx=x+x2. Definition: Floor function is the greatest integer that is less than or…

Q: Use a formula to express y as a function of t if y = 6x + 4x and x = t- 1.

A:

Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

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Q: Find the points of inflection of the function f(x)=e−x2.

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Q: 1. Plot the function f(t)= (x+5) for -35 x 3. 4+3x2

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

Q: 14. Use the curve sketching procedure to analyze the function. a. y-x'+x²-20x а. 1+x? b. y=- 1-x?

A:

Q: 1. Find the intercepts of the function. f(x)-x* +2 а.

A: Given data÷

Q: 2. Use the graph of the function f(x) to estimate where (a) f'(x)= 0, y f(x) (b) f'(x) 0.

A: (a) f'(x) =0   => the slope is zero, it means when the graph is parallel to x-axis  i.e. at…

Q: Use the graph of the function f to find approximations of the given values. y 4-

A: To find the values of f at x= a,  we imagine the vertical line x=a and where the vertical line…

Q: For this function Y=x^3 + 15x^2 -225x prove that we have a point of inflection at x=-5

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Q: Determine the range of the following functions. Express your answers using interval notation. y =…

A: Topic-function

Q: Find the absolute extrema of the function on the closed interval. 3 f(x) = x³ – , [-1,2]

A:

Q: Given the following function: y = x^4 - 8x^3 + 22x^2 - 24x + 2 on [0, 4], find the absolute extrema…

A: To find the absolute extrema of a continuous function on a closed interval [a, b]: Find all…

Q: 2 For what values of x does the graph of f(x) = 2x° + 3x – 180x – 1 have a horizontal tangent line?

A: First we find the derivative of f(x), the slope of f(x) for horizontal tangent is 0 and the…

Q: 10. Which is correct for the function f(x) = 2|x + 3| – 2? A. maximum (-3,-2) B. minimum (-3,-2) C.…

A:

Q: 1. Plot the function f(t): (x+5) for -35 x 5. 4+3x2

A: Plotting graph by finding slope.

Q: Determine the values of x at which the function in Figure  is: (a) discontinuous and (b)…

A: To determine the values of x at which the function is  a) discontinuous. b) nondifferentiable.

Q: Let f(x) = x2. Give an equation of the line that intersects the graph of f(x) at x = 0 and x = V2.

A: Given data:     The given function is: f(x)=x2. The first value of x is: x1=0. The second value of x…

Q: 16. Find the range of the function y = 1+ x2

A: Range: The range of the function is the set of all values of the dependent variable y corresponding…

Q: Answer the following questions for the function, r(x) x2 + 4x A) Is the point (0,0) on the graph of…

A: Given: r(x)=2x-10x2+4x

Q: What happens to the function f (x) = 1 + as x approaches to zero.

A: The definition of the function gx=x is given by, gx=x for x≥0=-x for x<0 Thus, the left hand…

Q: This is what I have so far but it says I am missing something.

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Q: Find the point on the curve g(x) = x² – 2 that is closest to the point (3,-2)

A: We can represent all the points on the curveg(x) = x2-2 as (x, x2-2)Now we will use the distance…

Q: The graph of f(x) and a line tangent to the curve at x = 4 are shown. If g(x) = V f(x), evaluate…

A: To find: The value of g'(4) if g(x)=f(x). Concept used: Chain rule: f(g(x)=f'(x)g'(x)

Q: Find and classify the extreme point of the function f(x, y) 3y2x + x³ - 3y3 - 3x? + 2.

A:

Q: Consider the function f(x)=(x+1)(x–1)2, At what value of x will the graph of f cross the y-axis?…

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Q: For which values of x does the graph of  f(x) = 8x3 - 12x2 - 24 have a horizontal tangent? Enter…

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Q: Find the intervals where the function f(x)= x^2e^3x is concave up.

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Q: Find the lineearization L(x) of the function f(x) = x^3/4 at x = 16.

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Q: Find k so that the function f(x) = x² + kx will be tangent to the line y = 2x-9

A: Here, the given function is: f(x)=y=x2+kx...(1) And also given that the tangent line to the given…

Q: Find the equation of the line tangent to the graph of f(x) = 3 - 2x at x = 3. Provide your answer…

A: The given curve is fx=3-2x and point is x=3 The slope of tangent on a curve f(x) at x=a is given by,…

Q: Write the equation of the line tangent to the graph of f (x) = -3x² + 5x + 1 at x = 1 and use it to…

A: We have to find the tangent line equation and also we have to approximate f(1.2).

Q: 2. Sketch the graph of the function (b) ƒ(x, y) = Vx² + y? – 1 -

A: our objective is to draw the graph.

Q: What is the x-value associated with the extreme point of the following function: 1*1.1^x+ 1*0.2^x?

A: Given Data: Function: fx=1×1.1x+1×0.2x The derivative of the given function is,…

Q: The function y is discontinuous at x equals? x+2

A: Given function is: y=x-4x+2

Q: Find the line tangent to the function at the indicated point: f(x) = v8x² – 4x ;x = 1 ОУ-12х-10 o…

A: Since there are multiple questions present and you have not specified which question to answer,…

Q: Find the curve length of the function 1 1. f(x) = ;x² 0 < x < 3

A: We can find the curve length as below.