Show that if f"(x) LO for XG [asb ] then

Q: If f"(x)>0 on an interval I then...

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Q: Suppose f is a function with property that f(x) ≤ x 2 for all x. Show that  f'(0) = 0.

A: Suppose f is a function with property that f(x) ≤ x2for all x. Showthat f'(0) = 0.

Q: Suppose f(x) = - 2x - cosr. (a) Show that f is strictly decreasing on R. (b) Hence, justify that 2x…

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Q: Find the values of a and b that make f continuous everywhere. x2 - 4 x - 2 ax2 - bx + 3 if x < 2…

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Q: Define f(x) = (x2 - 81)/(x - 9) at x = 9 so that the function becomes continuous at 9.

A: Concept: A definition of a function is that a relation from a set of inputs to a set of possible…

Q: -x²+5 < f (x) < x+1 2

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Q: Suppose that f(x) = βx2 − 3     if x ≤ 2                                βx + 2       if x &gt; 2…

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Q: Compute f(x) if f(x) = sin(2x).

A: Given,           f(x) = sin(2x)

Q: Define f(x) =(x2 - 81)/(x - 9)at x = 9 so that the function becomes continuous at 9.

A: Given function is fx=x2-81x-9. To define function fxso that the function becomes continuous at x=9.…

Q: Let f be defined as follows: x2 +5 for x > 5, Зах f(x)3D for xs5 For what value of a is the function…

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Q: Let f(x) = – 5 In(7x) f'(x) =

A: Given,           fx=-5ln7x

Q: Find f(") (x) given f (x) = In(x + 1)

A: Given function is  f(x) = ln(x+1)  We have to find the nth derivative of f i.e. fn. We use  notation…

Q: Let f(x) = 7 In(x). %3D Then f'(x) is andf'(3) is

A: Given that :  f(x)=7lnx

Q: Find the values of a and b that make f continuous everywhere. x2 - 4 if x < 2 X - 2 f(x) = if 2 < x…

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Q: The function f(x) = x^2 is decrea sin g on (- ∞,0)  True or False

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Q: If f ' ' ( x ) = 2 , then f ( x ) is concave up at x = 2 . True OR False

A: f(x) is concave up at x= k if f"(k)&gt;0

Q: Show that the function f(x) = K. when xw0 when xois discontinuous at x = 0.

A: Solution

Q: Suppose f is continuous on [1,5] and the only solutions ofthe equation  f(x)  = 6 are x = 1and x= 4…

A: Given: The function f is continuous on 1,5 and fx=6 has only two solution x=1, x=4 and f2=8, To…

Q: Determine if f is continuous at x 9 from the right. [5x² f(x) = 3x-27 if x <9 if x29

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Q: if x < 6 cx2 + 7x x3 - cx Let f(x) = if x 2 6. For what value of the constant c is the function f…

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Q: What is the function f on (a, b) if for all x1, X2 in (a, b) when x, f(x2). is it decreasing or…

A: for all x1 , x2 in a,b when x1&lt;x2 then fx1&gt;fx2 claim- is it decreasing or increasing

Q: how that the function  f(x)=x3-3x2+3x-100 is increasing on R

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Q: Let ƒ be the function given by ƒ(x) = (x-2)²(x+3). For what values of x is f not continuous?

A: The given function is fx=(x-2)2·(x+3)(x-2)·(x+1) We have to find the values of x, for which f is not…

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: Find the values of a and b that make f continuous everywhere. x2 - 4 if x < 2 X - 2 ax2 - bx + 1 4x…

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Q: Find the values of a and b that make f continuous everywhere. x² – - 4 if x < 2 X - 2 f(x) ax2 - bx…

A: Please refer the attached image for complete solution.

Q: how that: (f)=X*(-f) x(t) is even, then b₁=0, an= To

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Q: in of (fo f)(x). (Enter your answer using

A: We have to find the following conditions according to the given information

Q: Suppose that f(x) = 17ex - exe Find f'(3)= ?

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Q: Find f'(1) for f(x) = In(v6x – 3).

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Q: Suppose that f(x) = SBx? – 3 if if (Bx+2 x> 2 Find the value of B so that f(x) is continuous…

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Q: Suppose that f(x) = βx2-3     if x≤2                                   βx+2       if x &gt; 2…

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Q: Let f(x)={tan(2x) ax+b if x>0 if x<0 For which values of a and b is f(x) differentiable for every…

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Q: Find a function f(x), such that f"(x) = 3sin(4x). %3D

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Q: Suppose f(æ) = |x| · x Then f-l(x) = if æ > 0, and f-'(x) = if x < 0.

A: given that fx= x.xfind f-1x for x≥0 and x≤0

Q: Show whether f(x) is continuous (3х-2 f(x)={ x-2 x² -4 for x=- for x+ -

A: Given that, f(x) = 3x - 2; for x = - 2 f(x) = (x + 2)/(x^2 - 4); for x not equal to - 2 So when x is…

Q: 8 — х — x2 if x 4 -

A: f(4-) = 8 - 4 - 16 = -12 f(4+) = 2*4 - 20 = -12 f(4) = 8 - 20 = -12

Q: Compute f' (*) if f(x) =22x sin(x). 2

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Q: Find the function g such that fog = In (2x° +7) if f(x) = In x g(x) = %3D

A: Find the function g such that  f(g(x))= ln(2x3+7) and f(x) = ln(x) .

Q: Suppose f(x) = 4nx?e-Tx -e-n for all x € R. Show that f = -f. %3D

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Q: (b) Suppose that f(x) = ൜βx2 − 3    if x ≤ 2βx + 2      if x &gt; 2 Find the value of β so that f(x)…

A: For continuity, left hand limit=right hand limit=f(x)

Q: If f(x) = etan-r , then f' (x) :

A: Given: fx=etan2x we know that ddxex=ex

Q: Suppose f is a bounded real function on [a, b), and f' eR on [a, b). Does it follow that fe R? Does…

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Q: 4. If f(x) = sin x, show that f(2.x) = 2f(x)f(-x) %3D

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Q: Find f"(x) if f (x)=√√5 - 4x. Show work:

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Q: (b) Suppose that f(x) =  βx2 − 3            if x ≤ 2 βx + 2             if x > 2 Find the value of β…

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Q: Show that F(X) = Sin X ornot.

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Q: If f(x)=e^cosh(4x) then f'(x)=

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