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Question Video: Estimating the Derivative of a Function Using a Graph Mathematics • Higher Education

For the given graph, estimate 𝑓′(−1.5).

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Video Transcript

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.

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