Question

What does evaluating \[\left.\frac{dy}{dx}\right|_{x=x_0}\] give?

Options

• The value of \(x\) when \(y=0\)

• The rate of change of \(x\) with respect to \(y\)

• The instantaneous rate of change at exactly \[x=x_0\]

• The total change in \(y\) for every value of \(x\)

Answer 1

Evaluating the derivative at \[x=x_0\] gives the instantaneous rate of change at that exact value.
This is called the rate of change at a specific instant.