# F(x)=e^0.5x when x<=0 and f(x)=-(x-h)2+k when x>0 find h and k such that f(x) is both continuous and smooth at x=0?

##### 1 Answer

Feb 13, 2018

#### Explanation:

For the function to be continuous, you need its left hand and right hand limits to both match its value at

This means that

To be smooth the left hand and right hand derivatives must match at

So

Thus