6. Suppose that we don't have a formula for g(x), but we know that g(2) = 4 and g'(x) = Vx2 + 5 for all x. (a) Use a linear approximation to estimate g(1.95) and g(2.05). (b) Are your estimates in part (a) too large or too small? Explain.

Q: 4. Find the orthogonal trajectories of the given family of curves. y = cx'.

A: Solution:-              y=cx3 →          1              Diff. w.r.t x            ⇒dydx=3cx2…

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A: given cost functio cx=25600+100x=0.1x2

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A: 1st we will derive formula for O(h) and O(h2) and then find corresponding values

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A: Giveny= x2-3x-4 = f(x)at point ( 2, -6)as f(x) =x2-3x-yand f(2+h) = (2+h)2-3(x+h) -4…

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Q: Suppose that the total cost of manufacturing x units of a certain commodity is C (x) = 2?2 + 6? +…

A: Given, Total cost of manufacturing x units of a certain commodity =  C(x) =  2x2 + 6x + 12 We need…

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Q: The

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Q: 2. Find the orthogonal trajectories of the family of curves x2 + y² = 2my where m is a constant.

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Q: . Suppose that we don't have a formula for g(x), but we know that g(2) = 4 and g'(x) = Vx² + 5 for…

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A: Given, g(1)= -1 g'(x)= √(x²+15) g'(1)= √16= 4

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