Question

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. The function is f(x) = 4 sin(x), and the point is (0, 0).

Answer 1

The slope of the graph of the function at the point (0,0) is 4.

Step-by-step explanation:

The slope of a function can be found by taking the derivative of the function. For the function f(x) = 4 sin(x), the derivative is f'(x) = 4 cos(x). To find the slope at a given point, we substitute the x-coordinate of the point into the derivative. In this case, the point is (0,0), so we substitute x=0 into f'(x) to get f'(0) = 4 cos(0) = 4. Therefore, the slope of the graph of the function at the point (0,0) is 4.

We can confirm this result using a graphing utility by calculating the slope between two points on the graph. Let's choose the points (1, 4) and (-1, -4). The slope between these points is (4 - (-4))/(1 - (-1)) = 8/2 = 4, which matches the slope we found using the derivative.