Find the constants of A and B?

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Find the constants of A and B?

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Answer 1 · 2017-02-09T13:21:47

$(a, b) = (- 1, 6)$ $(a,b)=(-1,6)$

Explanation:

If $f (x)$ $f(x)$ is continuous for $- 3 \leq x \leq 0$ $-3 <=x <= 0$
then it is continuous at $x = - 2$ $x=-2$ and at $x = 0$ $x=0$

If $f (x)$ $f(x)$ is continuous at $x = - 2$ $x=-2$
then
$XXX f (x) = - x$ $color(white)("XXX")f(x)=-x$ at $x = - 2$ $x=-2$
$XXX \to f (- 2) = a \cdot {(- 2)}^{2} + b = - (- 2)$ $color(white)("XXX")rarr f(-2)=a * (-2)^2+b = -(-2)$
$XXX \to 4 a + b = 2$ $color(white)("XXX")rarr 4a+b=2$

If $f (x)$ $f(x)$ is continuous at $x = 0$ $x=0$
then
$XXX f (x) = 6$ $color(white)("XXX")f(x)=6$ at $x = 0$ $x=0$
$XXX \to f (0) = a \cdot 0^{2} + b = 6$ $color(white)("XXX")rarr f(0)=a * 0^2+b=6$
$XXX \to b = 6$ $color(white)("XXX")rarr b=6$

Combining $4 a + b = 2$ $4a+b=2$ and $b = 6$ $b=6$
gives
$XXX a = - 1$ $color(white)("XXX")a=-1$

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Find the constants of A and B?

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