(b) Suppose that f(x) = 2x^2 − x^4 . Find the intervals on which f is increasing and those on which it is decreasing.

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Q: Show that f-(A U B) = f-'(A) U f-'(B) and f-1(A n B) = f-'(A) nf-'(B) for any function f. Is the…

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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: Q2/Show that the functions is harmonic u = 2 x (1 - y)

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Q: Consider the function Suppose that g(6) = ƒ' (6) = f(x) = (1 + sin(x)) (*) -9 and g'(6) - 4.

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Q: If f(x) = - f'(x) = f'(5) = 2 sin r 3 + cos x 3 then

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Q: 3 (a) Differentiate the left-side functions with respect to the right-side ones I+/(1+x³), i) tan…

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Q: Find f" (x) if f (x) = tan(x² − 1). ○ 2 sec² (x² - 1) ○ 2 sec² (x² − 1) (1 + 4x² tan(x² − 1)) ○ 2…

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Q: f(x) = 8 cos x 5 tan x.

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Q: Let f(x) 39 27 O 1 4√3 O-√6 9 3√3 .-1 (²). Then the second derivative at x = -1,f"(-1), equals = COS

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Q: et f(x)=-11sin x+3 cos x f' (x)=?

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Q: Find f if f" (x) = 2 + cos(x), f(0) = -8, f(T/2) = 8. *(x) :

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Q: (x² +8) cotx 2 - cos x csc x Find f' (x) when f (x) = 2x cot x – (x² + 8) csc²x A. f' (x) = csc²x 4x…

A: As we know that; The Quotient rule: fg'=f'·g-g'·fg2 The Product rule: f·g'=f'·g+f·g' The…

Q: f(x) = 4sin (1-3x2) + xcosx-9, then f'(x) = -24xcos (1-3x2)+cosx-xsinx True O False

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Q: Prove that the function n = x(x^2 - 3y ^2)+ (x^2 - y^2) + 2xy is harmonic. Also find the conjugate…

A: Then,     and Thus,   and , it follows  that .Hence, the  given function is harmonic.(Proved)…