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I have to find all values of a and b for which the function will be continuous.

what I do is next: f(0)=1 ; limit of ax+b = b => b=1 ;

and I get stuck with a, can a be anything?

Leonardo
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1 Answers1

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Yes, you're right!

You only have to have $a0+b=1-0-0^2$, because $f$ obviously is continuous on $(-\infty,0)$ and on $(0,+\infty)$ as it is a polynomial.

So $a$ may be any real number, $b$ has to be equal $1$.

tong_nor
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  • thanks, and I have second part of the task where I have to find all values of a and b for which the function will be differentiable. so, derivative of f(x) at x=0 point is (-1+2x) => a= -1 and b must be 1? – Leonardo Mar 03 '16 at 18:04
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    Yes, first continuity. It gives $b=1$. Now you have to compute left and right derivative at point 0. https://en.wikipedia.org/wiki/Left_and_right_derivative The left one is $-1$, the right one is $a$. – tong_nor Mar 03 '16 at 18:07