a) Suppose that a state's income tax code states that the tax liability on x dollars of taxable income is given by, 0 if x <0 0.14 if 0

Q: 21. Determine the following function if continuous at 2x g(x) s6) = ; at x = 3 \x² – 4x + 3 A.…

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Q: DETERMINE IF THE FOLLOWING FUNCTION IS CONTINUOUS AT THE GIVEN VALUES OF X.  f(x) = 1/x^2 - 9  a.…

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Q: Under what circumstances can you extend a function ƒ(x) to be continuous at a point x = c? Give an…

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Q: Suppose that f(x) is differentiable function such that f(1)=3 and f(1)=4. If g(x)= f(x) -, then what…

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Q: determine the location and value of the absolute maximum and absolute minimum for the given…

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Q: Let C be a real number and let f(x) = 3 70 . If the slope of the tangent line to the graph of f(x)…

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Q: 1. Given the graph of f', the derivative of f, locate all extrema of f. JUSTIFY. Minimum at x =…

A: To find the minima and maxima from the graph of f'(x)

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A: When f'(x)&gt;0 then function increasing when f'(x)&lt;0 then function decreasing

Q: Determine the values of x at which the function in Figure 18 is: (a) dis- continuous and (b)…

A: (a) Here from the graph, we can see that, The graph has a break at the point x =1, that is, Thus…

Q: Answer the following True or False: If f(x) is a differentiable function such that f'( – 2) = 0,…

A: Given  f(x) is differential function  f'(-2)= 0   means x= -2 is critical point of f(x)

Q: 18. Suppose that f is a differentiable function such that f(g(x)) = x, and f'(x) = 1 1+(f(x))². Show…

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Q: if x3 is continuous at x = 3

A: Given query is to find the value of c so that function is continuous at x = 3.

Q: If an odd function f(x) has a local maximum value at X=c which of the following must be true?

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Q: Suppose f is a continuous function where f(7) = 9 and f'(7) = 6 . The tangent line to the graph of y…

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Q: (i) Discuss the continuity of the function f(x) = {x2 − 3x if x &lt; 2 2x + 4 if x ≥…

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Q: For all but two choices of a, the function (x) = x if xS a and x' ifx > a will be discontinuous at…

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Q: If a function contains a “jump,” occurring at a certain x value, then can the function be…

A: No function is not continues at this x.  Because function has jump discontinue at this x.

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

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Q: Determine if the given function is continuous at the indicated number x = c. |x-3| if x#3 4. j(x) =…

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Q: A type of discontinuity wherein the curve appears to the eye, to be continuous, but the single point…

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Q: 3. Sketch the graph of a function that is continuous, but not differentiable at I= 1.

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Q: The total number of local maximum and minimum points of the function whose derivative, for all x, is…

A: 1st derivative of function is f'(X) =x(x-3)^2(x+1)^4 For critical point we must have f'(X)=0 Hence…

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

A: To check for the continuity of the function fx=x2+2xx≤14-x1&lt;x&lt;3x-3x≥3

Q: x2-x-1 , if x 1 is 1 if x= 1 continuous at x=1 since the right and the left limits are equal at x =…

A: f(x)=x2-x-1if x&lt;13x3-4if x&gt;11if x=1

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

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Q: Give the formula for a function which has vertical asymptotes at x=7 and x = -6 but is otherwise…

A: A function has vertical asymptotes at x=7 and x=-6 but is otherwise continuous.

Q: Sketch the graph of a continuous function y =f(x) that satisfies the following conditions: 1. f'(x)…

A: This question is about graphing a function

Q: Determine if the given function is continuous at a given value of x. 2. f(x) = x² - 4x – 2 at x = 1…

A: Since you have posted multiple questions i can do first three subparts as per our company guidelines…

Q: Find the location of the indicated absolute extremum for the function. Minimum f(x) X = -1 O x = 2 O…

A: Here I am attaching image so that you understand each and every step.

Q: Answer the following True or False: If f(x) is a differentiable function such that f'(-4) = 0, then…

A: Given that the function f(x) is differentiable function and f'-4=0 We need to verify whether its…

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

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Q: 1. Give an example of a function f : R –→ R that is continuous and bounded but does not achieve…

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

Q: Suppose that f(x) is differentiable function such that f' (1)=8 and f (1)=4. If    g(x) = (f(x)) /…

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Q: Determine if the function is continuous or discontinuous at x=2. h(x) = x - 1, if x 22 2x- 1, if x<2…

A: if Left hand limit and right hand limit are equal then function is…

Q: 3) Find the value of k that makes function continuous at x = 4 Зх + 8 x > 4 f(x) = 4x – k x < 4 — k

A: A function is a relation from a set of inputs to a set of possible outputs where each input is…

Q: If g is a differentiable function that g(x) less than zero for all real numbers x, and if f'(x)=…

A: To analyze the extreme values (if any) of the function f(x) under the given conditions

Q: Is the following statement correct? If the function f is continuous at x=1, then the constant a…

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Q: If a function f is continuous at 0, show that g(x) = xf(x) is differentiable at 0 and find the value…

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Q: If a function is real and continuous in the region from a to b and f(a) and f(b) and if both have…

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Q: The function f(x) = 1+x has a local minimum when a = 0. Select one: O True O False

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Q: 20. Determine the following function if continuous at 2x g(x) = \72 – 4x + 3 . ; at x = -1 A.…

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Q: 5) Show that the function f(x)=-÷+1 below is continuous at x = -1. x-1 2- -3 -1- -2 1.

A: A function f(x) is continuous at x=c if  We have to show that is continuous at x=-1.

Q: Consider the piecewise-defined function Ax if x 0 h(x) е (a) Give values for A and B so that h(x)…

A: Given Data: Function: hx=Axif x≤0e-1/x+Bif x&gt;0 (a) The condition for the continuous function is,…

Q: _18. Determine the following function if continuous at f(x) = ) `x + 1' ; at x = 0

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Q: 2. Give an example of a function f: (0, 00) → K that is continuous and bounded but does not achieve…

A: It is an usual example which derivative not vanish anywhere

Q: There is an infinite discontinuity at x = 0 and f(0)=-2

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Q: If functions ƒ(x) and g(x) are continuous for 0&lt;=x &lt;=1, could ƒ(x)/g(x) possibly be…

A: According to continuity theorem if f(x) and g(x) are continuous on [0,1] then if g(x) ≠ 0 on [0, 1]…