Let f(x)= cases x^ 2 -4x+3, & 0 x<2

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

f(x)=\begin{cases} x^{2}-4x+3, & 0\le x<2,\\ x+1, & 2\le x\le 5. \end{cases}

The domain of interest is the interval

[0,5]

. (1) Part 1: (a) Identify and classify the discontinuity of

f

x=2

. Provide a brief justification. (2) Part 2: (b) Determine whether the Extreme Value Theorem applies to

f

[0,5]

. Give a reasoned explanation. (3) Part 3: (c) Find a subinterval of

[0,5]

on which the Extreme Value Theorem does apply to

f

. State the interval and justify your choice. (4) Part 4: (d) On the original interval

[0,5]

, compute the absolute maximum and minimum values of

f

(if they exist) and the

x

-values at which they occur. Discuss how your findings relate to your conclusion in part (b).