Question

the graph of a function f is shown above. at which value of x is f continuous, but not differentiable?
a ( a )
b ( b )
c ( c )
d ( d )
e ( e )

Explanation:

To determine where \( f \) is continuous but not differentiable, we analyze each point:

• At \( x = a \): The graph has a sharp peak (corner), so the derivative from the left and right will differ (not differentiable), but the function is continuous here (no break, hole, or jump).
• At \( x = b \): There is an open circle, so the function is not continuous (discontinuity).
• At \( x = c \): The graph is smooth (differentiable, continuous).
• At \( x = d \): There is a jump or hole (discontinuity).
• At \( x = e \): The graph is smooth (differentiable, continuous).

So \( x = a \) is continuous but not differentiable.

Answer:

A. \( a \)