1 if x < - 2 Sketch a graph of f(x) — х — 1 1 if -2 <х < 2 || - 2 if x > 2

Q: 1. Consider the function f(x) = x6 - x³. a. Determine the absolute extremum using the First…

A: The given function is fx=x6-x3. a. Find the absolute extremum using the first derivative test. b.…

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

A: Please see the below picture for detailed solution.

Q: 11. Find the absolute extremum of f (x) = 4- x3, where -2 < x< 1

A: Given: The function is  f(x)=4-x3,  -2≤x≤1   To determine: The absolute extremum of the function…

Q: 6x -4, xS 5 -kx + 6, If the function f (x) = is continuous at r = 5, then the value of k is --- --…

A: The given function is: This function is continuous at x = 5, if at this point left side limit,…

Q: (kx-1 ifx< 2 G(x) kx? if x 2 2

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Q: Let g be a function that is defined for all x, x # 2, such that g(3) = 4 and the derivative of g is…

A: Critical points of the function are the point either the derivative is not defined or derivative is…

Q: Sketch a graph of the function f(x) 2 sin(2x). %3D -77/8-31/4-5n/8-/2 -3/8-7/4-T/8 t/4 3n/8- /25/8…

A: Given function is f(x)=-2sin(2x)We know that period of sin(x)=2πThe period of sin(2x) will be π and…

Q: тӕ 11 if x - 4 If f(x) is a function which is continuous everywhere, then we must have = u

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Q: -x² +1 Let f(x) be defined as f(x)={* - | 1–sin² x if x20 if x<0

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Q: -x-2 if x2 h has an essential discontinuity at x = - 2 h has an essential discontinuity at x =2 (c)…

A: We are to determine whether the function has a removable or essential singularity at x=-2,2.…

Q: 5. Show that the function f(x)= 3x-9 is not differentiable at x=3. Find the formula for f'(x).

A: To Prove: Show that, given function is not differentiable at x = 3.…

Q: Sketch an odd function with a positive leading coefficient having all of the following features:…

A: We have to draw graph of given odd function.

Q: 11. Suppose that f(x) is differentiable everywhere and we know that f(-4) : f'(x) > 6 for all x. -2…

A: Part a) To find the least possible value of f(3), By the mean value theorem, Suppose f(x) is…

Q: x1 -1 if For what value(s) of x is the function f(x) = x+1 %3D (x² +x+1 NOT continuous?

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Q: 8. A restriction on the domain of f(x)=x²-9, so that f-¹(x) is also a function, could be 0-3≤x≤3…

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Q: 2. Let f(x)=1- x2/3. Show that f(-1)= f(1) but there is no number e in (-1, 1) such that f'(c)= 0.…

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Q: If f(x) < 0 for all real numbers x then f is decreasing on (-o, 00).

A: Proceed as shown below

Q: Sketch a graph of the function f(x) = 0.5 sin(3x). 4+ 2 -5/6 -27/3 -T/2 -T/3 -Tt/6 T/2 2/3 5/6 -1 -2…

A: Here is the solution

Q: The function f has a continuous second derivative, and it satisfies f(-6) = -1, f'(-6) = 0 and…

A: Maxima minima problem....

Q: 3 Find a formula for f-'(x) if f(x) = ( x – 1 x + 1 f-'(x) = (5-1)'(2) =

A: Solve the function

Q: 2x 10) Consider f(x) = 3-4 on the interval [2,6. Find the maximum and minimum values of f(x on the…

A: The given function is,

Q: 5. If f(x)=3*-9 and g(x)= tanx, then what is the domain of (g+f)(x) on the interval [0,2m]?

A: For the given question, we can write the function (f÷g)(x) as:f(x)g(x)=tanx3x-32Hence, the domain of…

Q: 2х — 2 Find (f-1)'(a) for f(x) = when a = — Зх — 1 - Enter an exact answer.)

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Q: 1. Find the absolute extrema of f (x) = x* - 8x² + 3 on the interval [-1,3].

A: Absolute extrema on a closed interval lies on end points or at f'(x) = 0 So first we have to…

Q: 1. Find the absolute max/min values of f(x) = 3x – 12r + 5 on the closed interval (0, 3).

A: Given the functionf(x)=3x2−12x+5,[0,3]

Q: Determine {f],where the periodic function is described by its graph. 19 2a 3a 40 (1-as) (1-) 1.…

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Q: 9. The graphs of power functions of the form f(x) = x", where n2 2 is an even integer, always…

A: Given: The graph of power function of the form f(x)=xn , where n≥2 is an even integer always contain…

Q: 11. Find the absolute minimum and maximum of f(x) = r3 - 4x2 - 3x + 3 on the interval [0, 4].…

A:

Q: The function f is decreasing on I if _____ when x1 < x2.

A:

Q: (2) f is monotone decreasing if and only if f'(x) < 0 for all r E I.

A: Here we will going to use mean value theorem  Mean value theorem (MVT) Suppose f(x) is a real valued…

Q: - Find f (x) given f' (x) 6x2 - 4x + 3 and (2, 15) is on the curve of f (x) .

A: To find the function from derivative we need to integrate.Here we will integrate to find f

Q: 10 % Let f(x) x- e-(a+1). Find the - second derivative and use it to determine the intervals on…

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Q: 19 – x² ; if x 3 continuous or not on the interval [0, 3].

A: Given function: fx=9-x2;if x≤3x-3;if x&gt;3 The objective is to determine if the function is…

Q: 9. Given the function f (x) = 3x -4x2 + 2, use the first and second derivative tests to find: a) the…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: Only question 21Explain why the function is discontinuous at the given number a. Sketch the graph of…

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Q: Consider the function f(x) = 2/x + 2 on the interval [4, 8]. Find th function on this interval.

A:

Q: 1) Find the absolute extremum values of f (x) = x² – 4x + 9 over the interval 1,4| -

A: Given,  fx = x2-4x+9    We have to find the absolute extremum values in the interval 1, 4

Q: 7. For the function f (x) = In(x² + 1) (a) find all intervals where f is increasing, (b) find all…

A:

Q: 12. Suppose we know that f (x) is continuous and differentiable on the interval [1,9], that f (9) =…

A: To find: The largest possible value of f1. Given: The fx is continuous and differentiable on the…

Q: Determine any critical point(s) for the function f(x)=  -3 / x2 - 9

A:

Q: 2. Define a function 6x2-x-15 3x-5 f(x) = |k, 3 (a) Find a value of k so that f(x) is a continuous…

A:

Q: 2. Find the value of k so that the function defined ( x2 + 4 x 2 - x = 2.

A: A function is a relation which maps each value in its domain to exactly one value in its range.…

Q: The graph of y = f(x) is graphed below. What is the end behavior of f (x)? 500 400 30 200 100 10 -8…

A: Analysing the graph of f(x) when the value of x is tending to infinity and-infinity

Q: [3 - x if xs 3 Let f(x) = - | 2x + 3 if x > 3' (a) Evaluate f(-2) and f(3). f(-2) = f(3) = (b)…

A:

Q: The function f(x)=(a-x)2/3 has domain R and only one critical point x= a. Use a number line to find…

A:

Q: 1 Let f(x) Find f'(x). 3 (z4 – )* - f'(x) =]

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Q: x²-a if x2 is continuous at x-2, then x+3 if x-2 If the function fo)

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Q: 11. Determine the absolute extreme values of f(x) = xe-/2 = xel-/2 on the interval [0, 5].

A:

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…