Interpret the derivative as the gradient of a tangent line of the graph of 𝑦 = 𝑓(𝑥).

Let \( f(x) = 2x^3 - 5x^2 + 3x - 1 \). (a) Determine the derivative \( f'(x) \). (1 mark) (b) Evaluate \( f'(2) \). (1 mark) (c) Interpret the value found in part (b) in terms of the graph of \( y = f(x) \) at \( x = 2 \). (1 mark)

Consider the function \(f(x) = x^3 - 6x^2 + 9x + 2\). (a) Determine the derivative \(f'(x)\). (1 mark) (b) Find the gradient of the tangent to the graph of \(f(x)\) at the point where \(x = 1\). (1 mark) (c) Interpret the meaning of your answer to part (b) in the context of the tangent line at \(x = 1\). (1 mark)

The function \(g(x) = x^3 - 6x^2 + 9x + 2\) has a stationary point at \(x = 1\). Which of the following statements correctly interprets the gradient of the tangent to the graph of \(y = g(x)\) at \(x = 1\)?