From the given we get this system:
.
The function f is defined by
f(x) = for
f(x) = for
Both f and its derivative are continuous for all values of x. Find the values of the constants a and b.
I find the derivative for both parts as
f'(x) = for
f'(x) = for
I know how to find a and b if they are continuous for one particular value for x - the function and the derivative are solved by means of simultaneous equations.
I tried to do this method for this question, but found that I achieved varying answers - I tried x=1, x=2 and this resulted in different values for a and b, so I'm guessing that this question requires something a bit different? How would you attempt to solve this?
Thanks for your help
And I solved this to get a = -1, b = 3.
But the question said that the function is continuous for all values of x - so shouldn't a and b be the same whatever value of x is used?
I've obviously misunderstood the idea of continuity, but I would like to know how my above statement can be proved wrong if it is