check all the x - values at which\na. (1 point) f appears to be not continuous\n□1 □2 □3 □4\nb. (1 point) f…

check all the x - values at which\na. (1 point) f appears to be not continuous\n□1 □2 □3 □4\nb. (1 point) f appears to be not differentiable. for each x - value you choose, give a reason why f is not differentiable.\n□1 reason: \n□2 reason: \n□3 reason: \n□4 reason:

check all the x - values at which\na. (1 point) f appears to be not continuous\n□1 □2 □3 □4\nb. (1 point) f appears to be not differentiable. for each x - value you choose, give a reason why f is not differentiable.\n□1 reason: \n□2 reason: \n□3 reason: \n□4 reason:

Answer

Explanation:

Step1: Recall continuity condition

A function is continuous at a point if the limit as $x$ approaches the point from the left equals the limit as $x$ approaches the point from the right and equals the function - value at that point.

Step2: Analyze $x = 1$

At $x = 1$, there is a jump - the left - hand limit and the right - hand limit are different. So the function is not continuous at $x = 1$.

Step3: Analyze $x = 2$

The function is smooth at $x = 2$, so it is continuous.

Step4: Analyze $x = 3$

The function is smooth at $x = 3$, so it is continuous.

Step5: Analyze $x = 4$

At $x = 4$, there is a jump - the left - hand limit and the right - hand limit are different. So the function is not continuous at $x = 4$.

Step6: Recall differentiability condition

A function is differentiable at a point if it is continuous at that point and the left - hand derivative equals the right - hand derivative.

Step7: Analyze $x = 1$

Since it is not continuous at $x = 1$, it is not differentiable. Reason: Not continuous.

Step8: Analyze $x = 2$

At $x = 2$, there is a sharp corner. The left - hand derivative and the right - hand derivative are different. Reason: Sharp corner.

Step9: Analyze $x = 3$

The function is smooth at $x = 3$, so it is differentiable.

Step10: Analyze $x = 4$

Since it is not continuous at $x = 4$, it is not differentiable. Reason: Not continuous.

Answer:

a. 1, 4 b. 1 Reason: Not continuous 2 Reason: Sharp corner 4 Reason: Not continuous