4. The position of a particle moving along a horizontal path is given by s(t) = t³ - 4t² - 3t+8, where t is in seconds. (a) Find the velocity and acceleration of the particle at any time t. (b) Determine the time interval(s) when the particle is speeding up or slowing down.

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A: Please refer to the image below

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A: topic- linearization of a function

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A: Given

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A: Follow the procedure given below.

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Q: approaching

A: Please refer to the image below

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A: Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: Topic = Area

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A:

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A: This question can be solved using the concept of Mean Value Theorem.

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A: Please refer to the image below

Q: company

A: Please refer to the image below

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A: Solution given below