How can we find the intersection points?

Question

We have the functions $f(x)=2\sqrt{x+3}$ and $g(x)=-0.5(x-1)^3+2$. I want to calculate the area between the graphs of the two functions above. For that we have to calculate the intersection points of the functions, but how can we find them in this case where we have a root and a cubic power? Could you give me a hint?

Answer 1

If you draw a graph of each function you will see there is just one intersection, around $x=-0.36$. I wonder if you don't actually mean a function $f(x)$ for if you mean the graph $y^2=4(x+3)$ you would have an area to calculate.

Answer 2

1.Plot the two functions using graphic calculator

2.Find the intersection the functions around x = -.358

3.Find the x intersects for the 2 functions respectively in this case , for f(x) is x = -3 and g(x) is x = 2.587.

4.Integrate the functions, for f(x) ,range from x = -3 to -.358 (remember to modules) it because it is in the negative x range, for g(x) , range from x = -.358 to 0(remember to modules) and g(x) from x = 0 to 2.587.

5.Finally add them together to get answer.