How do you find the minimal cost of a cost function?

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How do you find the minimal cost of a cost function?

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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You (generally) use calculus. You find the first derivative of the cost function with respect to the variable you're interested in and solve. Substitute the answer back into the original cost function to find the minimal value (all this assumes the second derivative of the cost function at that value is positive (which implies a minimum function value is found there)). Also, minima and maxima for functions may also be found at the boundary of the domain of the function. So if your cost function runs over all x in the set [0,1000], say, you should check the cost function at 0 and 1000 too.

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