# Thread: continuity and differentiability challenge problem

1. ## continuity and differentiability challenge problem

hey guys

the question is:

3ax - 7, x<2
ax^2 + bx + 1, x is greater than or equal to 2

find a and b so that the function is continuous and differentiable

i already put them equal to each other but at the end i get a-b = 4

2. ## Re: continuity and differentiability challenge problem

Originally Posted by ubhutto
the question is:
3ax - 7, x<2
ax^2 + bx + 1, x is greater than or equal to 2
find a and b so that the function is continuous and differentiable
i already put them equal to each other but at the end i get a-b = 4
If $f(x) = \left\{ {\begin{array}{rl} {3ax,} & {x < 2} \\ {ax^2 + bx + 1,} & {x \geqslant 2} \\ \end{array} } \right.$
You need to make $\lim _{x \to 2^ - } f(x) = \lim _{x \to 2^ + } f(x)\;\& \,\lim _{x \to 2^ - } f'(x) = \lim _{x \to 2^ + } f'(x)$