provide the matlab code that will exactly locate the two intersectionss between the curves.

f = @(x) 0.5*x^2 - 3*x + 9; g = @(x) 10*exp(x/10);

if method can be solved using fzero please use that

Answer 1

[Walter Roberson]

That problem cannot be solved. There are three intersections, not two, and the intersections locations are all at irrational (and possibly transcendental) locations. It is therefore not possible to exactly locate the intersections.

You should plot the functions to see that there are three intersections. They are at roughly -1/4, +10, +45

[Dan]

sorry in the question it says consider the first two roots. in the plot that was given for the question it only shows those two so i fugured there were only 2

[Walter Roberson]

Even if you consider only the first two roots, it is not possible to locate them exactly.

You should keep in mind for future that when you introduce exponentials into a functions over real numbers that you can expect to get exact solutions only if the linear portion equals 1 (exp(0)) or 0 (exp(-infinity))

[Dan]

hmm.. this was a question from an old exam so my prof must expect some sort of answer.. thanks for the help tho!

[Walter Roberson]

Sometimes teachers think of numeric solutions as "exact" solutions, but numeric solutions are seldom exact solutions.

fzero could certainly be used to get numeric solutions. A key trick here is to give it a range of values that it is allowed to search over, instead of just giving one starting point. See the fzero documentation.