Final answer:
To find the equation of the tangent line to f(x) = 3x at x = 5, we need to determine the slope of the tangent line and the y-intercept.
Step-by-step explanation:
To find the equation of the tangent line to f(x) = 3x at x = 5, we need to determine the slope of the tangent line and the y-intercept.
The slope of the tangent line is equal to the derivative of f(x) at x = 5. Since f(x) = 3x, the derivative is simply the coefficient of x, which is 3. Therefore, the slope of the tangent line is 3.
The point (5, f(5)) on the tangent line can be found by plugging x = 5 into the equation f(x) = 3x. This gives us f(5) = 3(5) = 15.
Using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we plug in the values m = 3 and (x, y) = (5, 15) to get the equation of the tangent line: y = 3x + b. Plugging in x = 5 and y = 15, we can solve for b: 15 = 3(5) + b. Simplifying, we get b = 0.
Therefore, the equation of the tangent line to f(x) = 3x at x = 5 is y = 3x.