Find the value for k so that the function will be continuous at x=4𝑥=4.f(x)=−8x2+64x−128x−4−73x2+24x+48+kifx<4ifx≥4
Question
Solution
To find the value of k that makes the function continuous at x=4, we need to set the two pieces of the function equal to each other at x=4 and solve for k.
First, plug x=4 into the first function:
-8*(4)^2 + 644 - 128 = -816 + 256 - 128 = -128 + 256 - 128 = 0
Then, plug x=4 into the second function:
-73*(4)^2 + 244 + 48 + k = -7316 + 96 + 48 + k = -1168 + 96 + 48 + k = -1024 + k
Setting these two equal to each other gives:
0 = -1024 + k
Solving for k gives:
k = 1024
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