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) = 7sin(x), and the point is (0, 0).

Answer 1

The slope of the graph of the function f(x) = 7sin(x) at the point (0, 0) is 7.

Step-by-step explanation:

To find the slope of the graph of the function f(x) = 7sin(x) at the point (0, 0), we need to calculate the derivative of the function with respect to x. The derivative of sin(x) is cos(x), so the derivative of 7sin(x) is 7cos(x). Evaluating the derivative at x = 0 gives us 7cos(0) = 7. Therefore, the slope of the graph at the point (0, 0) is 7.

To confirm this result using a graphing utility, plot the function f(x) = 7sin(x) and use the derivative feature of the graphing utility to find the slope at the point (0, 0). The slope should be equal to 7, which confirms our calculation.