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.
f(x) = 3/x^2 , (1, 3)
see Ms Sue's comment above
3+99
To find the slope of the graph of the function at a given point, you need to find the derivative of the function at that point.
To find the derivative of a function, you can use the power rule: d/dx(x^n) = nx^(n-1).
In this case, the function is f(x) = 3/x^2, which can be written as f(x) = 3x^(-2).
Applying the power rule, we can find the derivative of f(x) as follows:
f'(x) = -2 * 3x^(-2 - 1) = -6x^(-3).
Now, to find the slope at a specific point, let's substitute the x-coordinate of that point into the derivative we just found.
The given point is (1, 3), so we substitute x = 1 into f'(x):
f'(1) = -6(1)^(-3) = -6(1) = -6.
Therefore, the slope of the graph of the function at the point (1, 3) is -6.
To confirm this using a graphing utility, you can graph the function and its derivative. Enter the function f(x) = 3/x^2 into a graphing utility. Then, find the derivative of the function and plot it on the same graph. Check the slope at the point (1, 3) using the derivative feature of the graphing utility, which should confirm that it is -6.