Let-g-x-be-an-ininitely-differentiable-function-such-that-g-2x-6-g-3x-1-for-all-x-given-that-g-44-3-33-find-g-8-

Question Number 12246 by tawa last updated on 16/Apr/17

Let g (x) be an ininitely differentiable function, such that

g (2 x + 6) = g^{^{'}} (3 x - 1) for all x .

given that g (\frac{44}{3}) = 33 . find g^{″} (8)

Answered by mrW1 last updated on 16/Apr/17

u = 3 x - 1 \Rightarrow x = \frac{u + 1}{3} \Rightarrow 2 x + 6 = 2 \times \frac{u + 1}{3} + 6 = \frac{2 u + 20}{3}

g^{'} (u) = g (\frac{2 u + 20}{3})

g^{″} (u) = g^{'} (\frac{2 u + 20}{3}) \times \frac{2}{3} = \frac{2}{3} \times g (\frac{2 (\frac{2 u + 20}{3}) + 20}{3}) = \frac{2}{3} \times g (\frac{4 u + 100}{9})

g^{″} (8) = \frac{2}{3} \times g (\frac{4 \times 8 + 100}{9}) = \frac{2}{3} \times g (\frac{44}{3}) = \frac{2}{3} \times 33 = 22

Commented by tawa last updated on 16/Apr/17

God bless you sir . I need the cubic equation sir . formular .

i really appreciate your effort sir .

Commented by mrW1 last updated on 16/Apr/17

Commented by tawa last updated on 16/Apr/17

God bless you sir .

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