[5] True or false. If true, explain why. If false, give an example to show it is false: If f(x) is continuous at x=4, then it is also differentiable at x=4.

Q: (x2 -7 , 0b Is fdifferentiable at b?

A: Given that: f(x)=x2-7,       0<x≤b6/x   ,        x>b

Q: Find all extrema for f on the given interval. f(x): xE[-1,3] x+3

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Q: at

A: We have to choose the correct option from the given options according to the given information

Q: Use analytic methods to find the intervals on which the function below is increasing, decreasing,…

A: Given function, y=lnx ; -2≤x≤2, x≠0 To find the interval on which the function is increasing,…

Q: x+2 x<2 1) Let f(x)={ ax² – bx+3, ; 2sx<3 x 23 2x-a+b Find the values of the constants a and b given…

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

Q: 4. Given the graph and function below, complete the table. Differentiable Continuous f'(x)…

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Q: 3x2 – 1 if x1 Determine c and d so that f is continuous everywhere as indicated in the figure)

A: We have given;

Q: Let ​h(x)=​f(g(x)), where f and g are differentiable on their domains. If ​g(−1​)=2 and g′​(−1​)=7​,…

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Q: Lel f(x) = 2x (x² - 3x x 5 (a) Is f continuous at x = 5 ? (b) Is f differentiable at x = 5 ? (c) If…

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Q: Let f(x) + g(x) h(x) = x² – 3 As the followings are known for functions f(x), g(x) and h(x), what is…

A: ANSWER :

Q: Q:A Function is defined as follows sin f(x)= x +0 x = 0 what condition should be imposed on m so…

A: For the given function to be continuous , the conditions required is

Q: 56. Let G be a function given by [x³, for x s 1, G(x) = 13x – 2, for x > 1. a) Verify that G is…

A: Here given function as gx=x3for x≤13x-2for x&gt;1 Find left limit at x=1…

Q: The limit below represents the derivative of some function f(x) at some number a. 2(2 + h)* – 32 lim…

A: The derivative of the function fx at some number a is given by f'a = limh→022+h4-32h…

Q: true or false  if f(x) is continous at x=a, then f(x) is differentiable at x=a

A: False.    The given statement is not true in general.

Q: a. On what interval(s) is f(x) increasing? Justify. b. What is the concavity of f(x) at x=2?…

A: Part(a). From the given graph f(x) is increasing on the interval (-4,1) , Because f'(x)&gt;0   (…

Q: Let f(x) {2x? %3D + 4 if x > 1 (a) The value of a that will make f(x) continuous for all real…

A: Given function is fx=a+4x if x&lt;12x2+4 if x≥1 find the value of a, if f(x) is continuous. Is f(x)…

Q: x >0 If f(x) = { * then f is: x< 0 Select one: a. continuous at x=0 b. not continuous at x-0

A: For continuity at x = 0 check the left and right hand limit at this point.

Q: (-) = { kx + 5 for x 2

A:

Q: x² – 16 tate why f(x) is continuous on [1, 2]. x² – 9

A: f(x) is continuous on [a,b] if and only if  1. ∀x0∈(a,b)⊆R, limx→x0f(x)=f(x0) 2. limx→a+f(x)=f(a)…

Q: 2. Consider the function f(x) = x} – 5x. 5(r – 2) | (a) Show that the derivative is f'(x) = (b) Find…

A: Solve the following

Q: Find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the…

A:

Q: x² + 1, x 1 Let f(x) = Is function f continuous at x = 1? Is functionf differentiable at x = 1?

A: Given :-  f(x) = x2+1 when x&lt;1  f(x) = 4-2x when x≥ 1  To find:- Check function continuous or…

Q: 3x2 – 1 if x 1 Determine c and d so that f is continuous everywhere

A:

Q: Find a value of c that makes the following function continuous at x = 0. Explain why the value of c…

A: Given that, f(x)=15x-5sin3x2x3, x≠0c,                          x =0 The function is continuous when…

Q: 3. Given х— А ; х>1 f(x) = { 26+x – 3 3B ; x<1 Assume that f is continuous at x = 1. Find the value…

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Q: 4. Given the graph and function below, complete the table. Differentiable Continuous f'(x)…

A:

Q: 55. Let F be a function given by Sx2 + 1, for x s 2, 2x + 1, for x >2. F(x) = a) Verify that F is…

A: We have Fx=x2+1 ,  for x≤22x+1 , for x&gt;2 We have to verify   (a) Function is continuous at x=2…

Q: 3. Given X —А ; x>1 f(x) ={26+x – 3 3B ; x<1 Assume that f is continuous at x = 1. Find the value of…

A: If f(x) is continuous  at x=1 then limit must exist at x=1.

Q: Activity B. Determine if the following functions are continuous at the given value of x. Show your…

A: The three conditions of continuity of f(x) at x=a are, f(a) is defined. limx→af(x) defined…

Q: Find the values of c that make f continuous everywhere: ´x² – c² if a 9 smaller c = larger c = Use…

A:

Q: {x + 1, x < 4 lx - 4, x 2 4 Let f(x)= a) Explain why f is (or is not) continuous at x = 4. b)…

A:

Q: 3. At what points are the functions below continuous? x tan(x) x2+1 x+3 a) f(x) b) g(x) x2-3x-10

A: We have to find

Q: If f(x) is continuous on R, then |f(x)| is continuous on R.

A: Given that  If f(x) is continuous on R then |f(x) | is continuous on R.

Q: True or false? The function f(, y) is continuous at x² + y? the origin. O True False

A: We have to check three condition for continuity

Q: (x+1, l-x +1, x >0 Is f(x) continuous at x = 0? x30 Suppose f(x) =

A: We find the left-hand limit, right-hand limit and the value of f(x) at x=0

Q: a) For the function f(x) =1–3x² , find f'(a) at a =-1 by using the definition of derivative. (a + bx…

A: Integration means addition. It is used for adding a continuous function that cannot be added by…

Q: Sx²-x²+1 1-sin x if x20 ) Let f(x) be defined as f(x)={* 0>x Is f(x) differentiable at x = 0? a) Is…

A:

Q: Let f(x) be a function that is defined and has a continuous derivative on the interval (2, 00).…

A:

Q: The limit below represents the derivative of some function f (x) at some number a. 4(2 + h)° – 256…

A: We use the basic definition of derivative at a point. And compare with the given limit.

Q: The limit below represents the derivative of some function f(x) at some number a. 2(1 + h)° – 2 lim…

A:

Q: Sx + 1, x < 4 lx - 4, x 2 4 Let f(x)= a) Explain why f is (or is not) continuous at x = 4. b)…

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Q: |(2x + 1)(x – 2) for x + 2 S(x) = { x – 2 |k for x = 2 Let f be the function defined above. For what…

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Q: consider a continuous function y = f(x) whose first derivative is y = x(x – 2). The graph of f has…

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Q: Find where f(x) is increasing, decreasing, and find local extrema.

A: Differentiate the function fx=x2x2+1 with respect to x, to find f'(x) an f''(x).…

Q: For any function f with continuous derivative f', are the following statements true of false? For a…

A: We have to check the given integration is true or not.

Q: Find the absolute extrema for the function f(x)=x+ on the interval 0≤x≤ 6.

A:

Q: Is f(x) continuous at æ = a ? (Justify your answer). Determine whether f(x) is differentiable at z =…

A: Given that fx=3x2−4             x≥−11+2x                 x&lt;-1 To determine whether the function…

Q: H.W Ex 2: Determine if the f(x) is continuous at x = 3 ? [x² – 1 f(x)=- |x² + 2 at x=3 at x+3

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Q: Let f: R R be differentiable on some point c ER, then show that f(x+h)-f(x-h) f'(c) = lim 2h Show…

A: See the attachment

Q: x? + 2x + 1, if x 1. is continuous at x = 1 or not by using the definition of continuity.

A: f(x) = x2+2x+1  , if x≤14-x           , x &gt;1for a function to be continious at x = alimx→a+f(x) =…