Final answer:
To determine the equation of the line tangent to the function f(x) = (x - 3)(5 - x)³ at x = 4, we need to find the slope of the function at that point by taking the derivative. We can then use the point-slope form of a linear equation to write the equation of the tangent line.
Step-by-step explanation:
Determine the equation of the line tangent to the function f(x) = (x - 3)(5 - x)³ at x = 4
To find the equation of the line tangent to a function at a given point, we need to find the slope of the function at that point. The slope of the tangent line can be found using the derivative of the function. First, find the derivative of the function f(x) = (x - 3)(5 - x)³. Then, substitute x = 4 into the derivative to find the slope at x = 4. Finally, use the point-slope form of a linear equation to write the equation of the line tangent to the function at x = 4.