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Math Help - piecewise function

  1. #1
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    piecewise function

    f(x) = \left\{ \begin{array}{lll}<br />
x^2 + 2 x + 1 & \mbox{if} & x\le -2 \cr<br />
ax + b & \mbox{if} & x>-2<br />
\end{array} \right .

    This is differentiable at -2 .

    (a) It is known that if a function is differentiable at a point c, then it is continuous at c. Using now the continuity of f at −2, we can establish a relationship between a and b. Find this relationship and express it in the form b=Aa+B, where A and B are constants.

    Answer: b=2a+1

    b) Assuming x>-2

    \displaystyle \frac{f(x)-f(-2)}{x-(-2)}

    simplify into the form Ca+D, where C and D are constants. Find these constants.
    Answer: C=1, D=0

    c) assuming x<-2

    \displaystyle \frac{f(x)-f(-2)}{x-(-2)}

    simplify into the form Ex+F, where E and F are constants. Find these constants.
    Answer: E=1, F=0

    (d) Using the results of parts (a), (b) and (c), find the values of a and b.

    This is the part I don't understand how to do. The answer is allegedly -2 & -3.

    Can someone please explain how to do this part "D"?

    Thank you!
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  2. #2
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    Continuity gives -2a+b=1.

    Differentiability gives a=-2
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  3. #3
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    Got it, Thanks.
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