Stationary Point Derivative Notation Practice
Given the function \(f(x) = x^3 – 6x^2 + 9x + 15\), write the first derivative using correct derivative notation. Then, determine all values of \(x\) at which the function has stationary points.
Exploring Derivative Notations and Evaluating Derivatives
The derivative of a function can be expressed using different notations, such as f'(x) and \( \frac{dy}{dx} \). For the function where \(f'(x) = 3x^2\): (a) State the equivalent of f'(x) using \( \frac{dy}{dx} \) notation. (b) Find the value of \( \frac{dy}{dx} \) when x = 1.
Derivative Notation Comparison
Explain the differences, if any, between the derivative notations \(\frac{d}{dx}\), \(f'(x)\), and \(\frac{dy}{dx}\) and how they are used to represent the rate of change of a function.