(a) F'(x): arctan x, -8 T I (b) F(x)=0 if x <0, 1-e-x/ if x ≥ 0; 0≥0. x² 2 (c) F(x) = 0, if x < 0, if 0 < x < 1, 2x - x² 2 1, if 1

Q: Sketch the graph of a function that satisfies all of the given conditions. (a) f'(x) > 0 and f"(x) <…

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Q: x - x +2 4. If flx) =x + 7 find f'(x) . (5x - 1) (3x²) (A) (x' + 7)(5x - 1) – (x° – x + 2)(3x²) (B)…

A: The given function is  f(x) = x5-x+2x3+7

Q: Let f(x) I+5 f(x)

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Q: 1 •[₁ F(X) -1 Given f(x) dx = 0 and (a) [f f(x) and [₁ f(x) dx. 1 (c) [₁² (d) (b) • [² f(x) dx - [°…

A: (a)

Q: Given function f with f'(x)= 4-4x^2 / (x^2+1)^2 and f''(x)= 8x^3-24x / (x^2+1)^3 (a) Given the…

A: Given, f'(x) = 4-4x2(x2 +1)2  f''(x) = 8x3 -24x(x2+1)3 (a) If f is concave up then f''(x) &gt;0 So,…

Q: Find the absolute maximum/minimum if any of f (x)=x' +3x² +1 on the interval [-3, 2].

A:

Q: Q1/ Choose the correct answer: ( (1) The functions f. g and h are related by f(x) = g(x+1), g'(x) =…

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: f(x)=-(x-1)2 use f'(x) to find decreasing interval

A: f(x)=-(x-1)2 = - (x2 - 2x + 1) = 2x - x2 - 1

Q: Find value a  such that f(x)={x^2+2x-1 if x not equal to 1…

A: given,f(x)=x2+2x-1  if  x≠1a                if x=1left hand limit at x=1limx→1- f(x)=limx→1-…

Q: Suppose, f'(x)=2cosx+ sec x, -7<x<7½, and it is known that f(T) =D4. Find the function f(x). IT

A: Integrating on both sides, we get

Q: lim (x' – 2x* +5)= x→-2 O a. 22 O b. -11 O C. -13 O d. -18

A:

Q: If f(4) = 3 and f '(x) ≥ 3 for 4 ≤ x ≤ 7, how small can f(7) possibly be?

A: We have to find the smallest value of f(7)

Q: Find f'(x) and f'(c).

A:

Q: 6- y = f(x) 5. 4 3. y = g %3D 2)

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Q: f(x)= (ex+2 +1/e-x -14ex+1) / (xex-ex/x+1 +lnee^x) differentiate?

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Q: f(x) then: f'(x) = f'(1) -

A: We are asked to find the derivatives of the function.

Q: s defined by + x). The value o ind off to 1 decimal

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Q: Find (f-')'(@). 3 f(x) = x + x < 0, a = - 4 (f-1)'( – 4) = Preview

A: The given function is f(x)=x+3x and a=-4

Q: + If x? = x-y then, y *+y

A: Given  x2=x+yx-y first we multiply each side by x-y x2x-y=x+yx-yx-y     by dividing  x-y from x - y…

Q: Find (f-1)'(a) for f(x) = *+1 2x + 3 2 when a = 5 (Enter an exact answer.)

A: Take f^-1(x)=y. Then find f^-1(x).

Q: Find f'(x) and simplify. f(x)= Which of the following shows the correct application of the quotient…

A: We can solve as follows Do not confuse in round bracket and close bracket. They are same in this…

Q: 6. Find [ f(x)dx if f(x) = et -1, if -3<x<0 V9-x², if 0<x<3

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Q: Giren f(e) = 2x+1 and g(4) = x*+ 2x-1, in (- () Then valute he difcene hen x=2.

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Q: Given f'(x) = 4x³ + 12x², determine the interval(s) on which f is both increasing and concave up,…

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Q: 4. ƒ(x) = (x − 3)(x² + 6x-²) -√2: f'(x) 5

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Q: S(x) 르 arcsin (금x + 1) -3 Let f '(x) = . a Find f' (x) giving your answer in the form TV (bx(x + c)…

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Q: find f'(t) for f(x)=x/8x-8

A: We will need the quotient formula to find f'(x) Assume u and v, then find u' and v'

Q: 03: Let S(x)=12-x-1|-1. -1. Find f"(0) and Find f'(4)

A:

Q: (4) Consider f(x) = x5 + xª + 1. (b) On what intervals is f(x) one to one? (c) Find a formula for…

A: (d) Consider a given function: fx=x5+x4+1 Let gx=f-1x. Find g'1.0488 when domain of f is restricted…

Q: Зх-4 (5) Let f(x) x E [-2,2], find the absolute maximum and minimum x²+1 values of f(x).

A: We will find out the required value.