rate of fuel consumption

[audrey]

Hello, I have a problem that has 4 questions to it, and the background info for it is this:

Rate of fuel consumption recorded during an airplane flight is given by a twice-differentiated and increasing function R(t). The function is not given but the following table of values is given:

t,R(t)
0, 20
30, 30
40, 40
50, 55
70, 65
90, 70

Then the part of the question I'm struggling with is:

If the rate of fuel consumption is increasing fastest when t=45, what is the value of R''(45)? Explain.

I am confused about how to even start. How do you find R''(t) when you don't know what the function R(t) is?

Thanks so much!

 

[skeeter]

you were told in so many words that R'(t) is a maximum at t = 45 ... what what does that tell you about the derivative of R'(t) at t = 45?

... think about how you find extrema of functions in the first place.