3 years ago

PLZZ Help me algebra 2.

Mathematics

1 answer:

Kipish [7]3 years ago

7 0

Answer:

Step-by-step explanation:

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Determine the values of the constants b and c so that the function given below is differentiable. f(x)={2xbx2+cxx≤1x>1

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Assuming the function is

$f(x)=\begin{cases}2x&\text{for }x\le1\\bx^2+cx&\text{for }x>1\end{cases}$

For $f(x)$ to be differentiable, it necessarily has to be continuous. For this condition to be met, we need

$\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1^+}f(x)=f(1)$
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For the derivative to exist, the one-sided limits of the derivative must also exist and be equal. We have

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Now we solve for $b$ and $c$ :

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4 years ago