Question 1183693
<pre>
{{{matrix(1,3,
"f(x)",
""="",
system(matrix(2,2,3x^3-8x^2+8,x<-2,ax+b,x>=-2)) )}}}

The polynomial {{{3x^3-8x^2+8}}} takes on the value 
{{{3(-2)^3−8(-2)^2+8}}}
{{{3(-8)-8(4)+8}}}
{{{-24-32+8}}}
{{{-48}}} when x=-2

The polynomial {{{3x^3-8x^2+8}}} also has derivative
{{{9x^2-16x}}} and when x=-2, the derivative is
{{{9(-2)^2-16(-2)}}}
{{{9(4)+32}}}
{{{68}}}

So the line {{{y = ax+b}}} must join the polynomial {{{y = 3x^3-8x^2+8}}} 
at the point (-2,-48) in order for f(x) to be continuous there.  
Also the line must have the same slope as the polynomial has 
derivative there.  

y = ax + b  has slope a, so we have a=68

y = 68x + b

and it must pass through (-2,-48), so we substitute:

-48 = 68(-2) + b
-48 = -136 + b
88 = b

So a = 68 and b = 88.

Edwin</pre>