# Thread: Rate of change calculas

1. ## Rate of change calculas

Hey this is a double post im sorry the first post did not work.
I just cant work this one out. I was told I need to use the first derivative test, but i dont know how to apply to this question.

Help would be much appreciated as i have not done this level of maths in some time.

I am also aware i speled calculus wrong :P

The temperature of a chemical reaction is given by the formula

T(t)=8e^(-0.3(t-2)^(2))+7

where Tis the temperature and t is the time in seconds since the reaction was started.
a.
Draw a neat graph showing the reaction temperature during the first eight seconds of the reaction.
b.
What is the maximum temperature reached during this reaction?
c.
What is the maximum rate of increase in temperature achieved by this reaction? At what time is this rate achieved?

2. What work have you done so far?

I can give you hints..

a) Do you know what the function $f(x)=e^{-x}$ looks like in a plot of f(x) vs. x? If so, you should have some intuition into the nature of your temperature decay function.
What happens at t=0? You should be able to find the 'y' intercept.
Have you seen a Gaussian before? It is of similar form, $e^{x^2}$, perhaps your graph will look like a bell curve?

b) How do we find max's and min's in calculus? This is where you should take the first derivative, set it equal to 0.

c) Essentially they're asking at what point is the slope greatest. When you hear "slope of a function", your mind should think 'derivatives!'