for what values of a and c is the function differentiable at x=2?
f(x)= x+c, x>2
ax^2, x<(or equal to) 2
how do i start this problem? thanks so much
if the function is differentiable, then it has to be continuous ...
$\displaystyle \lim_{x \to 2^+} f(x) = \lim_{x \to 2^-} f(x)$
$\displaystyle 2+c = 4a$
also, since f(x) is differentiable at x = 2 ...
$\displaystyle \lim_{x \to 2^+} f'(x) = \lim_{x \to 2^-} f'(x)$
$\displaystyle 1 = 4a$
solve for $\displaystyle a$ and $\displaystyle c$.