The temperature of a sample of a fluid that is being heated in a laboratory is given by h(t) = 30t − t2 degrees Celsius, where t is measured in minutes and 0 ≤ t ≤ 5. (a) How fast is the temperature of the fluid increasing at t = 1 minute?  (b) When is the temperature of the fluid increasing at a rate of 20 degrees Celsius per minute?

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A: Here I am attaching image so that you understand each and every step.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.