Let the function f be defined by -5x + 4 for æ < -1 f (x) = x2 +3 for -1< x < 2 (1 %3D for a > 2 Evaluate f(-1)+ f(3)

Q: Suppose f'(x) = x² - 1. Then the graph of f is concave upward on 0 (-∞0,0) O (-1,1) (0,00) O (-∞,…

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Q: Suppose that the function f is defined on the interval (-2, 2 as follows. -1 if-2<x<-1 if -1<x<0…

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Q: 6. Let f(x) 1 Determine f(n)(x) 1- x

A: We have to find the nth derivative

Q: Find all numbers c which satisfy the conclusion of the Mean Value Theorem for the function f(x) = x…

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Q: For all x in the domain of f, f(-x) = f(x) Functions with this property are even functions Verify…

A: Note: in the above image, we have sum total of two questions which are the following.  (i)     (ii)…

Q: 1 Let f(x) x + 7 f-'(x) =

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Q: 3-64 -If f(x)=04 is the function continuous at x=4 x-4

A: If a function f(x) is given and we have to check continuity at x=a then we have to find LHL, RHL and…

Q: Find all numbers C in the interval [− 2, 2] guaranteed by the Mean Value Theorem for the function…

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Q: Let f(x) = (|x| + x2 − 1     if x ≤ 0          (|x| − x2 − 1     if x > 0 Is there some x in (−1, 1)…

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Q: 2, if x 0 Evaluate the piecewise function at the indicated values from the domain: f(x) = at x=-8…

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Q: Suppose that f(x) is a differentiable function such that f(4)-5 and f(4)=4. If g(x)=2xf(x), then…

A: Given f(x) is differentiable function such that f'(4)=5 and f(4)=4. Differentiating with respect to…

Q: 2) Let f be a function given by (3x +2 if f(x) = { 3 (x² + 1_ if Find f(0), f(-2), ƒ(-1), ƒ(1) and…

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Q: Explain why the Mean Value Theorem does not apply to the function f on the interval [0, 6].

A: Consider the function: fx=1x-3. Mean Value Theorem states that if a function is continuous on a,b…

Q: Find the absolute maximum and absolute minimum values of f on the.given interval. (4) f(x)= -3,31…

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Q: 7 Find the most general function F such that F'(): - 5V?.

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Q: find the largest domain for f(x) = (x-3)2   with an upper x bound of 8 such that the function f is…

A: fx=x-32 Differentiating with respect to x, we get f'x=2x-3 Now function is non decreasing in the…

Q: 9. If f (x) = prove that f (xr) is an even function. et -1 2

A: A function f(x) is said to be even if we have f(-x)=f(x)

Q: Determine if the piecewise function is continuous at a. x-3 x + 3 f(x) = 1, x-3 a = 3 x = 3 O Yes,…

A: Topic- limit

Q: A function for which f(x) = f( - x) for all x in the domain of f is called a(n) ____function.

A: The types of functions help to fill the given blank. The definition that consists of the terms f(x)…

Q: Does there exist a function f such that f(0)  =-1, f(2)  =4, and f'(x) ≤ 2  for all  x?

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Q: Select the graph of a function f that satisfies f' 0 on (-0, -1)U(-1, 0).

A: means f is decreasing for x&gt; - 1   means f(x) is concave up on both sides of x=-1

Q: 1 Let f(x) x + 13 f- (x) = |

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Q: Find the absolute extrema of the function on the closed interval.

A: We have to find absolute extrema of the function on the given close interval: fx=x3-32x2,    -1, 2…

Q: Let f(x) = 5x + 11 F^-1(x)

A: Given the function f(x) = 5x + 11 Find the inverse of the given function

Q: The function is said to be in this value if f(xo) 2f(x) for all x in an open interval. O Relative…

A: Given that: f(x0)≥f(x)

Q: Find the open intervals on which the function is increasing or decreasing         h(x) = √x(x − 3),…

A: For a critical point, we solve h'(x)=0

Q: Let the function F(x) = x³ - 5x² + 4x Define in a range of [-2.5]. Show that Rolle's theorem is…

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Q: Determine whether the function f(x)=5+3x if x <4…

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Q: 3- x, 3. f(x) = [-1,4] 3+x, x > 0 1 4. g(x) [-1, 2] .2 - 4

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Q: A piecewise function f is defind by [1-x, x1.

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Q: (4) Sketch the graph of a function f(x) satisfying (a) f(x) 2 and for x 0 for x between -1 and 2,…

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Q: Let f be the function (8x-1 for x х Find the values of a and b that make the function continuous.

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Q: (2) of the function f(x) such that F(1) = 4. Preview

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Q: Verify the Mean Value Theorem for the function f(x)=x(x- 1)(x- 2) in 0,3

A: Given fx=xx-1x-2 in 0, 3

Q: form the graph of f(x) into th 5) f(x) = x³ g(x) = -(x – 2)° %3D 3 %3D

A: We have to find

Q: Let f(x)=-3x-1, h(x)=-x+2. find (f o h)(-1)

A: Given  F(X) =-3X-1  h(X)  = -X+2

Q: 14. Determine if the function f(x)=2x°V4-x* is either even, odd, or neither (even nor odd). Does the…

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Q: Find the value of k so that the function f is k-x2 x3 X< 3 continuous at x=3 and f(x) х-8

A: Given, fx = k-x2x≤3x-8x&gt;3   We have to find the value of k so that function is continuous at x =…

Q: For all x in the domain of the function –* , x+1 this func- tion is equivalent to:

A: Since you have asked multiple questions in single request,  So we will be answering only first…

Q: Find the open intervals on which the function f(x)=x+4sqrt1-x is increasing or decreasing.

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Q: Let f be a real-valued function on R. Suppose that f(−1) = 3 and f'(x) ≤ 2 for all values of x. How…

A: f(-1)=3f'(x)≤2Integrating w.r.t x;∫ f'(x) dx ≤ ∫2 dxf(x)≤2x+Cf(-1)=33=2(-1)+CC=3+2C=5

Q: Find a function for which f'(x) exists for all real numbers but f"(x) doesn't exist for all real…

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Q: If the graph of a function f(x) is decreasing over the interval (a, b) then which of the following…

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Q: Let f(x)=x² defined a function on the closed interval −2 ≤ x ≤ 8. 1. f (4) 2. f(-3) 3. f (t – 3)

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Q: If f is differentiable and f'(x)=x³-2x²-x+2, then fis increasing or

A: Given, x³−2x²−x+2=f' We equate the given function to zero for critical points. x³−2x²−x+2=0   Step…

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

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Q: Suppose f(x) is differentiable everywhere and f(-3) Show f(1) > -6 and f(-5) -2.

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Q: The function of f is increasing on I if ______ when x1 < x2.

A: We have to find when function is increasing

Q: Consider the function f : {0, 1, 2,3, 4} → {0, 1, 2, 3, 4} defined by the formula f (x) = (x + 2) %…

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