Two runners start a race at the same time and finish in a tie. Prove that at some time during the race they have the same speed. [Hint: Consider f(t)=g(t)-h(t) , where and are the position functions of the two runners.

Q: (b) Solve for the optimum to the following problem using the Karush-Kuhn Tucker conditions: Optimise…

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A: The solution is given as

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A: Topic = Derivative

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A: Given that g(t)=|t|We can write it as:g(t)=t   , t≥0-t , t<0

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A: answer is in next step

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A:

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A:

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A:

Q: a. Find linearization of f(x) = Vx +1 at x = 7. b. Using your answer above, estimate V8.1.

A:

Q: Use differentials and the graph of f to approximate (a) f (1.9) and (b) f (2.04). To print an…

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Q: Where a is a constant, then a is equal to:

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A:

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A:

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A: Please rate and feel free to ask any query about any part of the question.  Thanks

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A:

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Q: Question 12 Find the linear approximation of the function f (x, y) = 2x – y + a²y - near the point…

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A:

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A:

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Q: (3) If | f(x) dx exists and c is a real constant, prove that f(2) dz = / f(x + c) dz. | {(x+c) Vel

A: As per our guidelines we are supposed to answer only one question. Kindly repost other question as…

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A: Wr have to find the derivative of the given function first.

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A: