Thread: Equalling Derivatives

Suppose the function g is defined by

g(x) = k for 0 [LaTeX ERROR: Convert failed] x [LaTeX ERROR: Convert failed] 3

= mx + 2 for 3 < x [LaTeX ERROR: Convert failed] 5

where k and m are constants. If g is differentiable at x = 3, what are the values of k and m.

this is part c on a question, but i dont think you need the information from the original question.
Thanks!

If it is given that is differentiable at , then both pieces of the piecewise function must have the same values of and .

So let's see where the two pieces are equal to each other when :




Making that substitution, let's see where the derivatives are equal to each other at :






So, is differentiable at . You can check your work to see that this piecewise function is continuous at with these constants and that there is a single value for with these constants.

Originally Posted by Pinkk

If it is given that is differentiable at , then both pieces of the piecewise function must have the same values of and .

So let's see where the two pieces are equal to each other when :




Making that substitution, let's see where the derivatives are equal to each other at :






So, is differentiable at . You can check your work to see that this piecewise function is continuous at with these constants and that there is a single value for with these constants.

thanks so much. its so simple once u explain it