How to find where a function is increasing at the greatest rateGiven the function f ( x ) = 1000 x 2 11 + x 2 on the interval [0,3], how would I calculate where the function is increasing at the greatest rate?

Question

How to find where a function is increasing at the greatest rateGiven the function   f  (  x  )  =            1000              x        2                    11      +              x        2             on the interval [0,3], how would I calculate where the function is increasing at the greatest rate?

juicilysv · Accepted Answer

Step 1Differentiating the function will give its slope. Since slope is defined as the rate of change, then getting the maxima of the function&#039;s derivative will indicate where it is increasing at the greatest rate.The derivative of f(x) is             22000      x              (      11      +              x        2                    )        2            .Step 2Applying the first derivative test, the critical number is             11      3      . The function increases before the critical number and decreases after it, so the critical number is a maximum.            11      3       is the answer.

Given the function f(x)=(1000x^2)/(11+x^2) on the interval [0,3], how would I calculate where the function is increasing at the greatest rate?

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