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BlackZzzverrR [31]
4 years ago
5

This is a question for my Calc 1 class at ASU.

Mathematics
1 answer:
Trava [24]4 years ago
7 0

The two pieces are continuous for every c \in \mathbb{R}

So, our only concern is to make sure that the pieces "glue" continuously at x=7.

To ensure this, we evaluate both pieces at x=7, and impose that the two values are equal.

The first piece evaluates to

f_1(7)=7^2-c = 49-c

The second piece evaluates to

f_2(7)=7c+1

So, we want

7c+1=49-c

We move all terms involving c to the left hand side, and all the numerical constants on the right hand side:

8c=48 \iff c=6

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