Correct f(x) is the velocity in meters per hour a snowmobile...

Correct f(x) is the velocity in meters per hour a snowmobile is traveling at x hours. Which of the following does the slope f'(x) represent? Answer Distance in meters the snowmobile has traveled in x hours. Direction the snowmobile is traveling at x hours. Average rate of change in the velocity of the snowmobile in meters per hour at x hours. Rate of change of the velocity of the snowmobile at x hours. Key

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00:01 In this question, even the position function of particle, we are asked to find the formula for its velocity, to find its velocity at x equals 0 and x equals 2, and find the values of x where its velocity equals to 0.

00:16 So, to answer the first question, we're basically given the formula already.

00:21 We just need to define the velocity, we need to differentiate the function f.

00:27 And we're asked to find the derivative of the function to 70x minus 18 x squared.

00:34 And to differentiate this function, we are simply going to use the power roll.

00:40 The derivative of 270x equals to 270 and the derivative of x squared equals to 2x.

00:56 We are going to get 270 minus 36x.

01:02 So this is v of x, velocity of the particle.

01:09 The formula is v of x equals to 270 minus 36x.

01:14 Now let's find the values of v at 0 and 2.

01:20 Of 0 equals to 270 minus 36 times 0 and equals to 270 and view of 2 equals to 270 and velocity at 270 minus 72 and equals to 198.

01:52 So velocity at 0 is to 70 and velocity at x equals 2 is 198.

01:57 So it's decreasing.

01:59 And let's answer the last question.

02:02 We are asked to find the points, the values of x, at which v.

02:06 Of x equals to 0.

02:08 So we just need to solve the equation v of x equals 0...

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