# help with this calc problem - differentiation, continuity, has variables

• Nov 2nd 2008, 04:55 AM
LexiRae
help with this calc problem - differentiation, continuity, has variables
y=
2x^2 + 3ax +1 if x is < or = 1
mx+a if x>1
what values for m and a make x continuous and differentiable at 1?

i know the basic process: solve for x, set the limits equal, differentiate those 2 equations. but i get stuck with all the variables.
thanks!!

EDIT** yeah youre right i fixed it. but can anyone help me answer it?
• Nov 2nd 2008, 05:20 AM
Nacho
are you sure that is mx+a if x>0? I think that should say x>1 :)
• Nov 2nd 2008, 06:09 AM
skeeter
$\displaystyle y = 2x^2 + 3ax +1$ if $\displaystyle x \leq 1$

$\displaystyle y = mx+a$ if $\displaystyle x>1$

for continuity ...

$\displaystyle 2(1)^2 + 3a(1) + 1 = m(1) + a$

for differentiability ...

$\displaystyle 4(1) + 3a = m$

solve the system for a and m.
• Nov 2nd 2008, 06:13 AM
Nacho
In general this problem solve whit skeeter method, only you know is that if the function is continue the lateral limit are equals :)