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Question
If f (x) is continuous on [–4, 2] defined as
f (x) = 6b – 3ax, for -4 ≤ x < –2
= 4x + 1, for –2 ≤ x ≤ 2
Show that a + b =`-7/6`
Solution
Since f is continuous on [-4, 2],
f is continuous on x = -2
`lim_(x->-2^-)f(x)=lim_(x->-2^+)f(x)`
`lim_(x->-2^-)6b-3ax=lim_(x->-2^+)4x+1`
`6b-3a(-2)=4(-2)+1`
`6b+6a=-7`
`(a+b)=-7/6`
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