Practicing Success
Practicing Success
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| Find the values of $a$ and $b$ such that the function $f$ defined by $f(x)=\begin{cases} 5& \text{if}\hspace{.2cm} x \leq 2\\ ax+b& \text{if}\hspace{.2cm} 2< x<10\\ 21,& \text{if}\hspace{.2cm} x\geq 10\\ \end{cases}$ is a continuous function. |
$a=3,b=5$ $a=2,b=1$ $a=1,b=2$ $a=4,b=3$ |
| $a=2,b=1$ |
| From the continuity at the point $x=2$ we get $2a+b=5$ and from the continuity at the point $x=10$ we get $10a+b=21$. Solving these two equations we get $a=2,b=1$ |
