Find the slope of the line that is tangent to the given function’s graph for the specified value of the independent variable. f(x) = 9x – 8; x=10.
To find the slope of the line that is tangent to the graph of a function at a specific point, you need to apply the concept of differentiation or taking the derivative.
Step 1: Differentiate the function to find its derivative.
The given function is f(x) = 9x - 8. To differentiate this function, we can use the power rule, which states that if f(x) = ax^n, where a is a constant and n is any real number, then f'(x) = anx^(n-1).
Using the power rule, we find the derivative of f(x) as follows:
f'(x) = d/dx(9x - 8) = 9.
Therefore, the derivative f'(x) of the given function f(x) = 9x - 8 is equal to 9.
Step 2: Substitute the given value of x into the derivative.
The problem specifies that we are interested in finding the slope of the tangent line at x = 10. So, substitute x = 10 into the derivative we found in Step 1:
f'(10) = 9.
Therefore, the slope of the tangent line to the graph of f(x) = 9x - 8 at x = 10 is 9.