x² + 1, if x < 1 3x, if x 1 is f(x)continuous at x = 1? Explain. 16 If f(x) %3D

Q: Use the First Derivative Test to locate the x-value of all extrema. Classify if it is a relative…

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Q: Determine if the function f(x) is continuous and/or differentiable at x = 1? x +5 for - 1sxS1 f(x) =…

A: The given function is f(x)=x+5    for -1≤x≤16x       for  1&gt;x≤4 The function is said to be…

Q: (mx²- -3x+1 f(x) = x + 1 of function x=1 continuous at the х-1 X = 1 point of What should m and n be…

A: The given function is, f(x)=mx2-3x+1x-1,x≠1f(x)=n,x=1. That is,…

Q: 1. Find the absolute extrema. 1) f(x) = 5 – x² on [-5,4]

A: fx=5-x2,  -5, 4 Differentiating with respect to x, we get f/x=0-2x=-2x Now to find critical numbers,…

Q: 2) The limit below represents the derivative of some function f(x) at some number a.…

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Q: Find the absolute extrema for f (x) = -x² – 1 over [-2,2] .

A: Please refer the attached image for complete solution.

Q: ,x5 (A) 5 (B -4 6 3 (E) none of the given choices

A: Given that, The function f(x) is following, f(x)=x-4,x≤5kx2-24x+46,x&gt;5 We have to find the value…

Q: Determine the intervals where the function f (x) = x ln x (x 7 0) is increasing and where it is…

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Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x ln…

A: Now differentiating with respect to x, we get

Q: 4x -5x-6 for x +2 Given f(x) 2-V2x 4 for x = 2 Is the function f continuous at x = 2 ? Give…

A: A function f(x) is continuous at x = a if limx→a+f(x)=limx→a-f(x)=limx→af(x).

Q: ( 2x -. Is g(x) continuous at 2?

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Q: 4. The graph of f' (x), the derivative of f of x, is continuous for all x and consists of five line…

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Q: 6-Iff is a continuous at x=c, then f has a derivative at x=c. * a. True b. False

A: Consider the given statement "If f is a continuous at x = c, then f has a derivative at x = c".

Q: Use the graph of the first derivative function f'(x) to find x values at which function has relative…

A: First of all, consider the graph of f '(x).

Q: Find constants a and b such that the function 3– bx, if x>-2 f(x)=- -1, if x=-2 ax – bx, if x<-2 |…

A: Given query is to find the value of a and b.

Q: Find the linerization  of f(x)=x^3  near x=1 . use that linerization to approximate (1.1)^3

A: Linearization of f(x) near x=a is given by f(x)=f(a)+f'(a)[x-a] Where f'(x) is first derivative of…

Q: True or FalseA 1. A Step-function is continuous at every point in its domain

A: Given: A step - function is continuous at every point in its domain. To write: The given statement…

Q: 2. f(x) = is a continuous function but it is discontinuous at x = 3. Explain why X - 3 this is not a…

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Q: 2. If function f(x) = 3²-12 is continuous at x=2, find f(x). x-2

A: We need to find f(x).

Q: (x² + 8, if x4) Consider the function f(x) = Find the value of B such that f (x) is continuous at x…

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Q: 3. The graph of the continuous function g, the derivative of the function f, is shown above. The…

A: Given problem is :

Q: 10 1. If :| f(x) dx = –7 and = 1 then determine 1- f(x) dæ || -3 -3 showing working.

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Q: x+4 Which will prove that f(x) = %3D x2+16 is continuous at C= -4? 1. f(-4)=0 II. lim f(x)=0 III.…

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Q: 1. If F(x) = - eta dt, find F(1) and F'(x).

A: If Fx=∫exe et2 dt, then to find F1 and F'x.

Q: x+1 Is the function f(x) - X2 *Xく2 ;ン2 x >2 2X-1 continuous at x= 2? Why or why not? Show solution.

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Q: The graph of f', the derivative of the function f, is shown below for the interval 0<xs10. The areas…

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Q: 7. If a continuous, differentiable function f has zeroes at x = -4, x = 1, and x = 2, what can you…

A: Mean value theorem relates average rate of change of a function over an interval to its…

Q: 2. Given the graph of derivative f'(x), find: a) Any interval (s) where f(x) is decreasing b) Any…

A: the function is decreasing when  as we can see from the graph,  on the interval  and  which means…

Q: х? — 4 if x 3

A: Given: fx=x2-4x-2,x&lt;2ax2-bx+3,2≤x&lt;32x-a+b,x≥3 We know that given function will be continuous…

Q: : Find the value of k that makes function continuous at x = 5 5x? – k x 5 f(x) =

A: Limit of a function at a point exists if the left-handed limit and right-handed limits at that point…

Q: Suppose we know that f(x) is continuous and differentiable on the interval [-7,0], that f(-7) = -3…

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Q: A continuous function y = ƒ(x) is known to be negative at x = 0 and positive at x = 1. Why does the…

A: Given that f(0)&lt;0 and f(1)&gt;0  f(x) is a continuous function.

Q: Find all the relative and absolute extrema of the given function on the given domain f(x) = x^2 +…

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Q: 3. Over which interval is the function f (x) = 1 + 2ex -3x increasing?

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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: 3. Give an example of a function with discontinuities at x =1 and x = 5.

A: To Find : A function that has discontinuities at x=1 and x=5.

Q: question. sf continuous at x = - 3? AY 5- 4- 3- 20 -5 -4 3 -2 -14 123 4 5 -2- -3- -4- -5-

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Q: Q3. Determine whether the function is continuous at x=1 or not (x² - 1 x = 1 f(x)=x-1 2, x = 1

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Q: 4. "The function f(x)= x-1 is continuous on(-o, 00)". Is the statement true or false? If it is…

A: Hi there, i have explain that if x tends to 1 from right side the function will give +1 and while…

Q: based off below graph true or false is f(x) is differentiable at x=3

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Q: 4. The graph of the first derivative f'(x) of a functionf is shown below. At what values of x does f…

A: Given graph of f'(x) is The value of x where f'(x)=0 are called as critical values where extrema…

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x2 -…

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Q: Suppose we know that f(x) is continuous and differentiable on the interval (-7,0], that f(-7)=-3 and…

A: fx is continuous and differentiable function on the interval -7, 0, f-7=-3 &amp; f'x≤2.

Q: D etermine if continuous f(x) = X-2 x² -14 %3D at x=2

A: Here we will check that given function is continuous at x=2 ,

Q: A function y = f(x) is decreasing on the interval [0, 5]. What conclusions can you draw about the…

A: A function is increasing, if when x increases, the value of y also increases.          Since the…

Q: Q20: . Suppose that f(x) is continuous and differentiable on the interval [0,6], that f(6) = -7 and…

A: Given that the function “f (x)” is continuous and differentiable on the interval [0, 6] that, f (6)…

Q: (2x - 2 x² - x f(x) = x² 4 graphing calcu x 2 x = 2

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