The table below shows y as a function of x, so that y f(x). According to the dat

Question

The table below shows y as a function of x, so that y f(x). According to the data in the table, is the derivative of f(x) negative or positive? Is the second derivative negative, positive, or zero? 10 20 30/40 50 (60 y f(x) 5 10 13 15 16 16.5 16.75 O The first derivative is positive; the second derivative is negative. O The first derivative is negative: the second derivative is positive. O The first derivative is positive; the second derivative is positive. O The first derivative is negative; the second derivative is negative. O The first derivative is positive; the second derivative is zero.

Explanation / Answer

The value of the function increases with x and so the first derivative is positive as the function is increasing but however the rate of increase decreases and so the second derivative is negative. The rate of increase decreases from 5 to 3 to 1 and so on.

Hence the correct answer is the first option.

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