If f(x) = 9 cos2(x), compute its differential df. df = (−18cos(x)sin(x))dx correct: your answer is correct. approximate the change in f when x changes from x = π 6 to x = π 6 + 0.1. (round your answer to three decimal places.) δf = .738 incorrect: your answer is incorrect. approximate the relative change in f as x undergoes this change. (round your answer to three decimal places.)

We want to find the differential of a function and also approximate the rate of change for a given interval.

We will get:

And the average rate of change in the interval [π/6, π/6 +0.1] is:

r = -8.191

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we have:

Now we need to differentiate it, we will use the rule:

Where:

Then we will have:

To estimate the rate of change between two values x = a and x = b, we must compute:

Here we will have:

a = π/6

b = π/ + 0.1

Replacing these we get:

If you want to learn more, you can read:

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a) t'(-3, 6) and v'(0, 3)  

step-by-step explanation:

a

step-by-step explanation: