Mary Jackson
2021-12-26
To make f differentiable everywhere, find an ang b.
Archie Jones
Beginner2021-12-27Added 34 answers
We are given
We want to ensure that the function can be varied everywhere. Since the two functions that make up this piecewise function are polynomials, they are continuous everywhere, which is necessary for this operation, the next thing we want to do is check for continuity at x=2.
And the second function gives us:
From here we know that for the function to be continuous it must be true that:
Next we also need make sure the functions first derivative has the same value when x=2, to do so we first find one:
From the second:
So for these two have the same value:
If we plug this in the first equation we found we get:
So our conclusion is for the given function to be differentiable everywhere a and b must take the values
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