Differentiable

• Oct 25th 2010, 11:44 AM
mmfoxall
Differentiable
This is a multi-step question, and i really don't know how to even start.:(

f(x) = x^2 - 4x + 1 if x <= 2 and ax + b if x > -2
Is differentiable at -2.

It is known that if a function is differentiable at a point 'c', then it is continuous at c. Using now the continuity of f at -2, we can establish a relationship between a and b. Find this relationship and express is in the form b = Aa + B, where A and B are constants.

• Oct 25th 2010, 11:51 AM
Also sprach Zarathustra
Quote:

Originally Posted by mmfoxall
This is a multi-step question, and i really don't know how to even start.:(

f(x) = x^2 - 4x + 1 if x <= 2 and ax + b if x > -2
Is differentiable at -2.

It is known that if a function is differentiable at a point 'c', then it is continuous at c. Using now the continuity of f at -2, we can establish a relationship between a and b. Find this relationship and express is in the form b = Aa + B, where A and B are constants.