If f x is differential function satisfying 6 x -01 f xt dt -2 x 3-3 x 2-6 x -5- thenA- f x is symmetric about x -1 - 2B- f x -0 has no real rootsC- f x -1 - 2 has two real rootsD- f x is minimum at x -1 - 2

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If f x is dif...

Question

If f(x) is differential function satisfying $6 x \int_{0}^{1} f (x t) d t = 2 x^{3} - 3 x^{2} + 6 x + 5$ , then

f(x) is symmetric about x = 1/2

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f(x)=0 has no real roots

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f(x) = 1/2 has two real roots

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f(x) is minimum at x = 1/2

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If f(x) is differential function satisfying 6. $\int_{0}^{1} f (t) d t = 2 x^{3} - 3 x^{2} + 6 x + 5,$ then

f (x), g (x)

[0, 2]

f^{''} (x) = g^{''} (x), f^{'} (1) = 2 g^{'} (1) = 4

f (2) = 3 g (2) = 9

f (x), g (x)

[0, 2]

f^{''} (x) = g^{''} (x)

f^{'} (1) = 2 g^{'} (1) = 4

f (2) = 3 g (2) = 9

y = f (x); x \in [0, 2]

\frac{d^{2} y}{d x^{2}} = 6 x - 4, f (x)

5

x = 1

f (x) = x^{13} + x^{11} + x^{9} + x^{7} + x^{5} + x^{3} + x + 12.

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