The graph of the function f is shown below. Of the following options, at what values of x is the…
The graph of the function $f$ is shown below.
Of the following options, at what values of $x$ is the function $f$ NOT differentiable?
(a)At $x = 0$ and $x = 2$
(b)At $x = 1$ and $x = 3$
(c)At $x = -1$ and $x = 1$
(d)At $x = -1.5$ and $x = 1.5$
Answer
Answer
Correct option: (a)
Answer: (a) At $x = 0$ and $x = 2$
At $x = 0$ the graph has a break (open circle at $(0,-1)$, the curve passes through $(0,0)$), so $f$ is discontinuous. At $x = 2$ the two arcs meet at a sharp point with vertical tangents, so there is no finite derivative. At $x = -1, 1, 1.5, 3$ the curve is smooth.
