Question

the derivative of the function f is given by f(x)=x² - x + 3. find the gradient of the tangent to the graph of f at the point where x = 2. give an exact answer as an integer.

Explanation:

Step1: Recall the formula for the gradient of the tangent

The gradient of the tangent to the graph of \(y = f(x)\) at \(x=a\) is given by \(f^{\prime}(a)\).

Step2: Substitute \(x = 2\) into \(f^{\prime}(x)\)

Given \(f^{\prime}(x)=x^{2}-x + 3\), when \(x = 2\), we substitute \(x\) into the derivative function:

$$
LATEXBLOCK0
$$

Answer:

\(5\)