Suppose f(x) > 0 and g(x) > 0 and that | f(x)dx diverges. If f(x) > g(x), what can we conclude about | g(2)dz? O It converges It diverges We can make no conclusions

Q: x if x20 If Ax) = -x2 then f'(0) if x <0

A: Given function, fx=x2      if x≥0-x2   if x&lt;0

Q: If f(-1) = 4 and f'(x) ≤ 5 for all x, what is the largest possible value of f(6)?

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Q: Suppose that a particular function f satisfies f" (x) = 12x? + 6x + 8, ƒ(0) = 1, f' (0) = –1. Then…

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Q: Suppose f(x) f'(2) = ex x² +5 . Find:

A: Given: f(x)=exx2+5

Q: 2. The graphs of the functions f and g are shown below on the same axes. If h(x) (8(x))4 wh f(x³) 12

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Q: 7. If f(x)=√(1-1²)et² dt, on which interval is f decreasing?

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Q: 0.6z Express the function h(x) = Ve' - 3 in the form h(x) = (ƒ o g)(x) where f(x) # x and g(x) ± x…

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Q: If f(1) = 4 and f '(x) ≥ 1 for 1 ≤ x ≤ 4, how small can f(4) possibly be?

A: If a function is continuous on some closed interval  and differentiable on the open interval  then…

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: If f(x) -6₁² = 2 f'(x) =| t³ dt then

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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: Let f(x)=√4x² + 4x + 6 f'(x) = f'(5) =

A: To find f'(x)

Q: The graph shown below is f(x)=√x+1.If g(x) = f(t)dt, find g '(3). 5 4 3 2 X 5 4 3 2 1 1 2 3 4 5 कृ…

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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: (vii) If f(1) = 10 and f'(x) > 2 for 1 < x < 4, how small can f(4) possibly be? Give proper…

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Q: If f'(x) = g'(x) for 0 < x < 1 then f(x) = g(x) for 0 < x True False

A: Topic:-  application of derivatives

Q: If we let f(x) = 1-4x/1+4x What are.... f’(5) = f”(5) = f”’(5) =

A: we have to find derivative at that point

Q: 2. Suppose that f(x) is an unknown function, but we know that g(x) = (x² + 5)(f(x))². (a) Find…

A: Using product rule of derivatives.

Q: If f(4) = 9 and f'(x) > 2 for 4

A: Solution: Given that f(4) = 9 and f'(x) 2 for all 4  x  6 If a function is continuous on some…