Thread: 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

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 . Next, the left and right derivative must equal so . Two equation and two unknowns.

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 ...






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





solve for and .