continuity and differentiability challenge problem

**ubhutto** · November 21st 2012, 07:34 AM

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

can someone please help me find out how to solve it, if it is even possible

**Plato** · November 21st 2012, 07:56 AM

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
can someone please help me find out how to solve it, if it is even possible

If $f(x) = \left\{ {\begin{array}{rl} {3ax,} & {x < 2} \\ {ax^2 + bx + 1,} & {x \geqslant 2} \\ \end{array} } \right.$

You need to make $\lim _{x \to 2^ - } f(x) = \lim _{x \to 2^ + } f(x)\;\& \,\lim _{x \to 2^ - } f'(x) = \lim _{x \to 2^ + } f'(x)$

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