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.

1 answer

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
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