Suppose that ƒ is a continuous and differentiable function s 2000 and that f'(x) > 7 for all x. What can you say about f(4)?

Q: We note that F is continuous for all x, and its derivative is (x-1) if x>0 F'(x)= -1 if xr<0 The…

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Q: 53. Is the function given by Sx + 1, for x << 4, f(x) -x + 7, for x 2 4, continuous at x = 4? Why or…

A: Given a function, f(x)=x2+1,      for x&lt;4-x+7,     for x≥4 To find whether the function is…

Q: Suppose f is continuous on an interval containing a critical point c and f 1c2 = 0. How do you…

A: The critical point of  f is x=c and f'c=0.

Q: The tangent line to y=f(x)y=f(x) at (−3,−2)(−3,−2) passes through the point (−4,−3)(−4,−3). Compute…

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Q: Suppose that a PDF for a continuous variable X is given by if 0 x)=3/4

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Q: 4 Determine if f (x) = - 2x if x 1 is differentiable at a = 1.

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Q: : Verify Mean value theorem for the function f(z) = 4x over the interval [0, 2].

A: As given function is: fx=4x3 Given interval is: 0,2 According to mean value theorem for a continuous…

Q: Suppose that the FIRST DERIVATIVE of a function f is given by f' (x) = (x – 3)² (z² + 5x). Find the…

A: We find the critical numbers by solving f'(x)=0

Q: If f(x) = etan-¹(x²-3) then f'(x) at x = 2 is equal to

A: SOLUTION-

Q: 1. Show that the function f(x) = 3x + 2 is continuous at (-2, 3). Is it uniformly continuous?

A: As per our guidelines we are mandated to solve only one question at a time please repost the…

Q: Given the piecewise function f(x) = = Why is f not differentiable at x = 4? Of has no tangent line…

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Q: 51. Is the function given by G(x) 1 continuous at x = 0? Why or why not?

A: Given: Gx=1x To check whether the given function is continuous at x=0

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: If - 2x +1 ,when X#! and fcx)= 3 when x= 1 show that The function fex) Continuous at X - 1

A: The detailed solution is as follows below:

Q: . Show that the following function is differentiable everywhere on R but of which the derivative is…

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Q: Let f(x)=x² – 3x'. For what value(s) of x in [–1, 1] is the slope of the line tangent to the graph…

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Q: Suppose that f is a differentiable function with f(2)=5. If the tangent line to the graph of y= f(x)…

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Q: Suppose that f(x) is a continuous function on the interval [0, π]. If f(x)=(sin x)² for 0<x<, then…

A: Since the f(x) is continuous function in [0, π], therefore the value of function at x = 0 must equal…

Q: for x 2 - X Is differentiable at x = 2 but not at x = 1.

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Q: How many continuous functions f are there which satisfy (f(x))² = x² for all x?

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Q: State both the converse and the contrapositive of the assertion “Every differentiable function is…

A: We will make use of fundamental definition of these terms.

Q: 2, if x 1

A: The given function,  f(x)=1x,if x≤1x2-1,if x&gt;1

Q: 56. Is the function given by Sx + 1, for x 4, G(x) = continuous at x = 4? Why or why not?

A: As we know that  Function will be continuous at x=a if limx→a-fx=limx→a+fx=fa

Q: Is the function given by f(x) = 5X+6, for x s5, 5x-14, for x>5, continuous at x=5? Why or why not?

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Q: Suppose /has a continuous derivative on the interval [0, 6]. Assume also that f' is increasing on…

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Q: Suppose that  f is a twice differentiable function (the function has a second derivative…

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Q: 9. Is the function defined by gon3 – 3 if 2. continuous at r= 2? differentiable at x = 2?

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Q: 3 Show that f(x)= 1x-5 is NOT differentiable at 5 by using the defini tion of the derivative, (Start…

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Q: Show that the function f(x) = exp(-|x|) is not differentiable at x = 0.

A: Given function is  fx=e-x given point is x=0.

Q: 4. Show that the function is continuous on (-00, 0). f(2) = {0 x* sin(1/x) if x 01 if x = 0 S

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Q: Suppose that f hits every value between y = 0 and y = 1 on the interval [0, 1]. Must f be continuous…

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Q: Suppose f is continuous on an interval containing a critical point c and f"(c) = 0. How do you…

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Q: 4. Determine if 1 1 sec if – 1 1 x – 1 is continuous or not at x = 0 and 1. In the case of…

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Q: Consider the function fcx) = (メフチ 5 E- xet X if x >5 if メ=5 5-X S> X f! Is fe) continuous at x=5?…

A: NOTE: Refresh your page if you can't see any equations. .

Q: let  f(x)=  x+2  if x1 Find the value of k that will make f continuous on (-∞,∞)

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Q: Show that the function xsin f(x)%D 0, When x 0 is continuous but not differenti able at x = 0 When x…

A: Let f be a function defined in the neighbourhood of 'a'. Then the function f is said to be…

Q: Give a formula of a continuous function that is differentiable except at 0.

A: Consider the provided question, For a function to be continuous at a point x=a, we say that the same…

Q: The tangent line to y=f(x) at (−8,−5) passes through the point (−3,10). Compute the following f(-8)…

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Q: 5. Is the function given by F(x): = x = -1? Why or why not? Vx continuous at

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Q: Find the length of the curve defined as: f (x) = 5x from x = 0 to x = 1

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Q: Suppose f is continuous on an interval containing a critical pointc and f″(c) = 0. How do you…

A: According to the second derivative test, If c= critical value. if f''(c)&lt;0, then f(x) has local…

Q: Suppose f(x) is a continuous function with f(-2) = 4 and f(1) = -1. What can we conclude about

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Q: Is f continuous at x = 1?

A: The condition of continues function is, limx→a+fa=limx→a-fa=fa   For limit of function from the…

Q: *** Use the first and second derivative to sketch the graph of f(x) = In(x² +1). In particular,…

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Q: (i) Consider the function such that f(x) = 2x if 0SxS1 and f(x) = x-1 if x> 1. Is f continuous over…

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Q: What value should be assigned to f(2) so that the extended function is continuous at x=2

A: Given graph of f(x)