Question

Do you agree or disagree with the statement “the instantaneous rate of change of the function f(x) = ln(x) / x5 at the point (1,0) is 1” ? Show working to support answer.

Answer 1

Find the derivative via quotient rule. Then evaluate the derivative at x = 1. Do you get 1?

Work it out and you'll see that it is 1.

Answer 2

derivative of ln x = 1/x
derivative of x^5 is 5x^4

Answer 3

so how you get 1 from that

Answer 4

what is the derivative of the function (using the Quotient Rule)?

Answer 5

[(x^5)(1/x) - (ln x)(5x^4)]/x^10

Evaluate at x = 1, you should get 1 (since ln 1 = 0).

Answer 6

how you get X^10

Answer 7

The quotient rule says, that the denominator is (x^5) squared, which is x^10

Answer 8

ok thanks ..... so where do the coordinates (1,0) come in?

Answer 9

we are interested in the x-coordinate x = 1.

The instantaneous rate of change is simply the derivative at x = 1.

Answer 10

oh I replaced x which is equal to 1 into quotient rule and I got 1

Answer 11

exactly, so the statement is true.

Answer 12

Thanks very much