1. ## ap calc

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

2. Originally Posted by holly123
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
Well, first it must be continuous so $4a = c+2$. Next, the left and right derivative must equal so $4a = 1$. Two equation and two unknowns.

3. Originally Posted by holly123
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 ...

$\lim_{x \to 2^+} f(x) = \lim_{x \to 2^-} f(x)$

$2+c = 4a$

also, since f(x) is differentiable at x = 2 ...

$\lim_{x \to 2^+} f'(x) = \lim_{x \to 2^-} f'(x)$

$1 = 4a$

solve for $a$ and $c$.