Originally Posted by
pantera Hello, I need help finishing this problem. Use one-sided limits to find values of the constants a and b that make the piecewise function differentiable at the point where the function rule changes.
f(x) = e^(ax), if x <1
and
f(x) = b + ln x, if x>1
Here's what I have so far.....
For f to be continuous at x = 1,
lim as x goes to 1 from the left of e^(ax)= lim as x goes to 1 from the right of (b+ ln x)
implies e^(a)=b
For f to be differentiable at x = 1,
lim as x goes to 1 from the left of ae^(ax)=lim as x goes to 1 from the right of (1/x)
implies ae^(a) = 1
So I'm having trouble solving for a and b for these two equations....
e^(a)=b
ae^(a) = 1
The solution says solve by grapher: a = 0.5671....and b = 1.7632....,
but I don't know how to get that.
Thanks