Hi everyone, this is a problem from a previous exam. I manage to solve half of it, but am struggling with the second half.
f(x) = x^{2} + x - 1 for x ≥ 0
f(x) = a cos(x) + b sin(x) for x < 0
Find a and b so that f(x) is continuous and differentiable for all x = 0
Can someone help solve this?
Thank you all!
Thanks for the help, I did that. Let me see, derivative on the right is 2x + 1 and on the left -sin x + b cosx. When I put them equal to each other and x = 0, I got b = 1.
In the answer key it says the opposite values, it says that a = 1 and b = -1. I manged to get that answer too by using another method. Perhaps it does not matter if the values of a and b are switched around ? (lol, I always think that).
Ok, I solved it both ways now do you know why the answers are switched around when we use this method?
And btw, I really like your signature ^^
Since a = -1, the left derivative is sin(x) + b cos(x), but since sin(0) = 0, the sign of sin(x) does not matter.
a = -1 and b = 1 gives the red graph, while a = 1 and b = -1 gives the blue one.
Perhaps the textbook authors thought that the left function is a sin(x) + b cos(x).
Thanks!