Question

(a) sketch a line that is tangent to the graph at x = 3 on the graph above.
(b) list all values of x where the slope of the tangent line to the graph of y = f(x) would be 0

Explanation:

Step1: Recall tangent - line concept

A tangent line to a curve at a point touches the curve at that point. For part (a), at \(x = 3\), we draw a line that just touches the curve at \(x=3\).

Step2: Recall slope - zero condition

The slope of the tangent line to the graph of \(y = f(x)\) is zero at the local maxima and minima. These are the points where the function changes from increasing to decreasing or vice - versa.

Answer:

(a) Sketch a line that touches the curve at \(x = 3\) on the given graph.
(b) \(x=2,x = 4\)