A friend concludes that because y = ln 6x and y = ln x have the same derivative, namely dy/dx = 1/x, these two functions must be the same. Explain why this is incorrect. Choose the correct answer below. A. A derivative shows the function\'s y-intercepts. Even though the function y = ln 6x and y = ln x have the same derivative, the derivative only shows that the functions have the same y-intercepts. B. A derivative is a measure of how a function changes as its input changes. It is incorrect because the derivative shows how the function changes at an equal rate, not that the functions are not the same. C. A derivative shows the function at a certain point. Even though the function y = ln 6x and y = ln x have the same derivative, the derivative only shows that the function are the same at a certain point. Solution A derivative shows the function\'s y- intercepts. Even though the fuction y=ln(6x) and y=ln(x) have the same derivative, the derivative only shows that the fuctions have the same y-intercepts.

1. A friend concludes that because y = ln 6x and y = ln x have the same derivative, namely dy/dx =
1/x, these two functions must be the same. Explain why this is incorrect. Choose the correct
answer below. A. A derivative shows the function's y-intercepts. Even though the function y =
ln 6x and y = ln x have the same derivative, the derivative only shows that the functions have the
same y-intercepts. B. A derivative is a measure of how a function changes as its input changes. It
is incorrect because the derivative shows how the function changes at an equal rate, not that the
functions are not the same. C. A derivative shows the function at a certain point. Even though the
function y = ln 6x and y = ln x have the same derivative, the derivative only shows that the
function are the same at a certain point.
Solution
A derivative shows the function's y- intercepts. Even though the fuction y=ln(6x) and y=ln(x)
have the same derivative, the derivative only shows that the fuctions have the same y-intercepts