the graph of f is given. select the x - values at which f is not differentiable with the correct reason(s)…

the graph of f is given. select the x - values at which f is not differentiable with the correct reason(s). (description: graph comprised of two components. first component rises in the 2nd quadrant, turns sharply downward at (-2, 4) continues to fall intersecting y = 2 to an open dot at (1, 1). the second component begins with a solid dot at (1, -2.5) and rises. it rises vertically through x = 3 and continues to rise through the 1st quadrant. ) 3, function not defined -2, function not defined 1, function not defined 3, vertical tangent 1, discontinuous

the graph of f is given. select the x - values at which f is not differentiable with the correct reason(s). (description: graph comprised of two components. first component rises in the 2nd quadrant, turns sharply downward at (-2, 4) continues to fall intersecting y = 2 to an open dot at (1, 1). the second component begins with a solid dot at (1, -2.5) and rises. it rises vertically through x = 3 and continues to rise through the 1st quadrant. ) 3, function not defined -2, function not defined 1, function not defined 3, vertical tangent 1, discontinuous

Answer

Explanation:

Step1: Recall differentiability conditions

A function is not differentiable at points of discontinuity, sharp - corners, or where there is a vertical tangent.

Step2: Analyze (x = - 2)

At (x=-2), the function has a sharp corner. The slope of the function changes abruptly from positive (as it was increasing in the second - quadrant) to negative (as it starts decreasing after the corner). So, the function is not differentiable at (x = - 2) due to the corner.

Step3: Analyze (x = 1)

The function has a jump - discontinuity at (x = 1). The left - hand limit and the right - hand limit of the function as (x\to1) are not equal. The left - hand limit approaches (y = 1) (open dot) and the right - hand limit approaches (y=-2.5) (solid dot). Since the function is discontinuous at (x = 1), it is not differentiable at (x = 1).

Step4: Analyze (x = 3)

The function has a vertical tangent at (x = 3). As (x) approaches (3), the slope of the secant lines approaches infinity. So, the function is not differentiable at (x = 3) because of the vertical tangent.

Answer:

-2, corner 1, discontinuous 3, vertical tangent