`f(theta) = 4sin(theta) - theta, (0,0)` Find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results.

Textbook Question

Chapter 2, 2.2 - Problem 37 - Calculus of a Single Variable (10th Edition, Ron Larson).
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kalau | (Level 2) Adjunct Educator

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Take the derivative.  Be careful that the derivative of theta with respect to theta is one!

`f'(theta)= 4cos(theta)-1`

Substitute the point given to determine the derivative:  ` `

`4cos(0)-1= 4(1)-1=3`

The graph of the derivative function,, is:

We can easily see that the derivative at zero is 3.

 

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