4. Show that: f(x) = 2²²₁ x+1 f'(x) = = 4x (1+x²)(1+x)(1-x) (x¹+1)² a. What are the critical points for f(x) on domain à € (-∞, ∞)? b. What is the maximum value of f(x)?

Q: Suppose f(): R" → R, G(.) : R" → R", and H(.) : R" → R² are functions. Consider the optimization…

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A: Given ,  The graph of f'(x) . To find all the local minimum points of f(x)  :-

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Q: f"(x) = 13r- (x²-1)a 2.f(x) = f'(x) = r* +1) 4x (x²-1)2 Determine the intercepts. Determine the…

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Q: 13. Let f be the function defined by f(x) = xe*. What is the absolute maximum value of f? (A) 0 1…

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

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Q: Q7. Let f(x) = x- In(1+x) 1+z on (-1; +∞0). (a) Draw the sign table for the derivative of f. In…

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Q: (c) Find the specific solution to d²y dx² when x = 0,= 0 and y = 1 +4 dy dx + 5y = 0

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Q: Find the absolute maximum value of the function f(x) = 5(x - e

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A: (A)Calculation of critical point of g(x):we can find derivative We can see that f(x) is positive and…

Q: 5. Given f(x) = Vx – 3 and g(x) = 3x* – x? + 2, find %3D a) (f•g)(x) b) g(F(x)) = Domain:

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