1
The Graph of 𝑓′(𝑥)
Notice that since the derivative at a point 𝑥 = 𝑎 is the slope of the tangent line
to the graph of 𝑓(𝑥) at 𝑥 = 𝑎, we can say something about the graph of the
derivative, 𝑓′(𝑥), simply by looking at the graph of 𝑓(𝑥).
Ex. Below is the graph of 𝑦 = 𝑓(𝑥). Sketch a graph of 𝑓’(𝑥).
2
𝑦 = 𝑓(𝑥)
𝑥
−2 −1 0 1 2 3
2
𝑦 = 𝑓′(𝑥)
1
𝑥
−2 −1 0 1 2 3
−1
−2
, 2
Ex. Below is the graph of 𝑦 = 𝑔(𝑥). Sketch a rough graph of 𝑔’(𝑥).
𝑦 = 𝑔(𝑥)
𝑦 = 𝑔′(𝑥)
The Graph of 𝑓′(𝑥)
Notice that since the derivative at a point 𝑥 = 𝑎 is the slope of the tangent line
to the graph of 𝑓(𝑥) at 𝑥 = 𝑎, we can say something about the graph of the
derivative, 𝑓′(𝑥), simply by looking at the graph of 𝑓(𝑥).
Ex. Below is the graph of 𝑦 = 𝑓(𝑥). Sketch a graph of 𝑓’(𝑥).
2
𝑦 = 𝑓(𝑥)
𝑥
−2 −1 0 1 2 3
2
𝑦 = 𝑓′(𝑥)
1
𝑥
−2 −1 0 1 2 3
−1
−2
, 2
Ex. Below is the graph of 𝑦 = 𝑔(𝑥). Sketch a rough graph of 𝑔’(𝑥).
𝑦 = 𝑔(𝑥)
𝑦 = 𝑔′(𝑥)
