For the given graph, estimate 𝑓
prime of negative 1.5.
Let’s mark on the graph the point
where 𝑥 equals negative 1.5. And we want the value of the
derivative at this point. Let’s recall that the derivative 𝑓
prime of 𝑥 is the slope of the tangent line to the graph at the point 𝑥. So, let’s try and draw on the
tangent line at our point.
We want to draw a line that follows
the general direction of the curve at the point negative 1.5. It would look something like
this. It’s a horizontal tangent line. This means that at our point
negative 1.5, the derivative is zero. And so, we can estimate that the
value of 𝑓 prime of negative 1.5 is zero.