Math help :( I feel dumb

[Q]

I have a test coming up, and am doing a review sheet (not graded, not HW).

I'll throw up an easy question: G(t) = .844t^3 + .918t^2 + 38.001 points is a student's grade when the student studies for t hours. Find G'(t)

I did, then it asks Find G'(4) and write a sentence of practical interpretation. 47.856 is G'(4).

Now all the actual math is simple b/c I've done all this before (ended up taking a higher level math class prior to this one, long story) but I always get confused on the stupid sentence writing.

So what is G'(4) telling me?

 

[chuckywang]

Originally posted by: Quintox
I have a test coming up, and am doing a review sheet (not graded, not HW).

I'll throw up an easy question: G(t) = .844t^3 + .918t^2 + 38.001 points is a student's grade when the student studies for t hours. Find G'(t)

I did, then it asks Find G'(4) and write a sentence of practical interpretation. 47.856 is G'(4).

Now all the actual math is simple b/c I've done all this before (ended up taking a higher level math class prior to this one, long story) but I always get confused on the stupid sentence writing.

So what is G'(4) telling me?

It tells you how much a student is improving his/her grade when he/she is at the 4 hour study mark.

 

[Q]

Originally posted by: chuckywang

Originally posted by: Quintox
I have a test coming up, and am doing a review sheet (not graded, not HW).

I'll throw up an easy question: G(t) = .844t^3 + .918t^2 + 38.001 points is a student's grade when the student studies for t hours. Find G'(t)

I did, then it asks Find G'(4) and write a sentence of practical interpretation. 47.856 is G'(4).

Now all the actual math is simple b/c I've done all this before (ended up taking a higher level math class prior to this one, long story) but I always get confused on the stupid sentence writing.

So what is G'(4) telling me?

It tells you how much a student is improving his/her grade when he/she is at the 4 hour study mark.

Ah yes that's it, I forgot the derivative is the instantaneous rate of change. durrr thanks

 

[halik]

Having studied for 4 hours, how much will you grade improve if you study more (or conversely, how much would your grade suffer had you stopped little before 4 hours)

 

[magreen]

To make it more concrete: "After you've already studied 4 hours, approximately by how much would your grade improve with an extra hour of studying."

See, that 47.8 number is a linear approximation of how much benefit an hour of studying gives your grade point. It's the slope of the curve at t=4, and slope=rise/run. Your gpa would be approx. 48 pts. higher at 5 hours than at 4 hours (just an approximation of course... since the function is curving, a whole hour is much too coarse of a sampling for the approximation to be very close to the actual curve).