Help me with this question!?

Question

If f(t) is the quantity in grams of a chemical produced after t minutes and g(t) is the same quantity in kilograms, then f'(t) = 1000g'(t).

Please explain to me wheter this statement is true or not.

f ' (t) means the derivative of the function f and
g ' (t) means the derivative on function g

Answer 1

First, we can agree that f(t) = 1000g(t), right?

If I produce 1000 grams after one second, that is the same as 1 kg. So in this example f(1) = 1000 and g(1) = 1. f(1) = 1000 * g(1). In general f(t) = 1000g(t).

But you asked about the derivatives of the two functions.
Let's imagine the functions were:
g(t) = t^3 + t^2 + 8
f(t) = 1000 (t^3 + t^2 + 8)

This satisfies the first statement.

Now take the derivative of both:
g'(t) = 3t^2 + 2t
f'(t) = 3000t^2 + 2000t = 1000 ( 3t^2 + 2t )

So f'(t) = 1000*g'(t).

Stated more simply, the derivative is the slope or the "rate" of change in the function. For every point, the rate of change of f(t) will be 1000 times the rate of change of g(t), because the measurement in grams is 1000 times the measurement in kilograms.

Answer 2

it's true, the rate of producing grams will be 1000 times greater than the rate of producing kilograms

Answer 3

False. If f(t) is grams and g(t) is killograms, then 1000*f(t) = g(t).