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When doing a question such as:

What is the area of the region enclosed by the graphs of f(x) = x - 2x^2 and g(x)= -5x?

what is an easy way to tell if a function is above or under the other, so I can tell which function to put first in the integral. MUCH APPRECIATED!

  • calculus -

    I hope you found that the two functions intersect at
    x = 0 and x = 3

    so pick any value of x in that domain,
    say x = 1
    f(1) = 1 - 2 = -1
    g(1) = -5
    since f(x) is above g(x) for that value,
    f(x) will be above g(x) for all values between 0 and 3

    If you had two functions that would intersect at more than 2 values of x, you would have to test this for each of the regions.

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