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 function's graph at a specific value of the independent variable, we can use the derivative of the function.
Step 1: Find the derivative of the given function, f(x), with respect to x. The derivative represents the rate of change of the function at any given point and gives us the slope of the tangent line.
The derivative of f(x) = 9x - 8 can be found by using the power rule, which states that the derivative of x^n (where n is a constant) is n*x^(n-1), and the derivative of a constant is zero.
Differentiating f(x) = 9x - 8:
f'(x) = (9 * 1) = 9
Step 2: Evaluate the derivative at the point where we want to find the slope, which is x = 10. Plug in the value of x into the derivative we found in step 1.
f'(10) = 9
The slope of the tangent line to the given function's graph at x = 10 is 9.