Asked by Anonymous
Piecewise function problem.
Let f(x)={ax^2+1/3, x is greater than or equal to 1; bx-10/3, x<1. If the function is differentiable, find the sum of a+b.
Let f(x)={ax^2+1/3, x is greater than or equal to 1; bx-10/3, x<1. If the function is differentiable, find the sum of a+b.
Answers
Answered by
Steve
f(x) =
ax^2 + 1/3 for x >= 1
bx - 10/3 for x < 1
so, we need f(1) to be consistent. That is,
a + 1/3 = b - 10/3
we also need f'(1) to be consistent:
2a = b
so, a + 1/3 = 2a - 10/3
a = 11/3
b = 22/3
a+b = 11
ax^2 + 1/3 for x >= 1
bx - 10/3 for x < 1
so, we need f(1) to be consistent. That is,
a + 1/3 = b - 10/3
we also need f'(1) to be consistent:
2a = b
so, a + 1/3 = 2a - 10/3
a = 11/3
b = 22/3
a+b = 11
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.