Find k so that the following function is continuous on any interval: f(x)= kx 0 (less than or equal to) x (less than) 2 3x^2 2 (less than or equal to x) i know the answer is 12 but i don't know how to arrive at that

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Question

Find k so that the following function is continuous on any interval: f(x)= kx 0 (less than or equal to) x (less than) 2 3x^2 2 (less than or equal to x) i know the answer is 12 but i don't know how to arrive at that

Find k so that the following function is continuous on any interval:

f(x)= kx
0 (less than or equal to) x (less than) 2

3x^2
2 (less than or equal to x)

i know the answer is 12 but i don't know how to arrive at that. could you please walk me through the steps? thanks.

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Answer 1

Answer #1

kx and 3x^2 are continuous where they apply. What you have to to is make sure they both give the same value at x=2, where one functional form changes to the other.

Thus require that 3x^2 = kx at x = 2.

3*4 = 2k

k = 6. The value of the function at x=2 is 12.

answered by: markiysha

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Answer 2

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Find k so that the following function is continuous on any interval: f(x)= kx 0 (less than or equal to) x (less than) 2 3x^2 2 (less than or equal to x) i know the answer is 12 but i don't know how to arrive at that

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Find k so that the following function is continuous on any interval: f(x)= kx 0 (less than or equal to) x (less than) 2 3x^2 2 (less than or equal to x) i know the answer is 12 but i don't know how to arrive at that

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Find k so that the following function is continuous on any interval: f(x)= kx 0 (less than or equal to) x (less than) 2 3x^2 2 (less than or equal to x) i know the answer is 12 but i don't know how to arrive at that