Question

I am having a hard time with a question involving optimization. Could someone help me with an exercise?

Answer 1

Sure, is this in Calculus 1 or 3?

Answer 2

Calculus 1

Answer 3

So what's giving you trouble? I love optimization problems, they're pretty fun once you get the hang of them.

Answer 4

If only I could master them like you XD lol Anyway here is the question...

Answer 5

Consider a toy car that moves back and forth on a long, straight track for 4 minutes in such a way that the function s(t)=96t-84t^2+28t^3-3t^4 describes how far the car is to the right of the starting point, in centimeters, after t minutes.

When is the toy car accelerating the fastest to the right? When is the toy car accelerating fastest to the left?

Answer 6

I am not sure how to start exactly. I feel like I should take the second derivative of the problem but I am not sure.

Answer 7

So you're on the right track (no pun intended) since you're given the position, the second derivative will be the acceleration.

But when is the acceleration the largest? Take a look at this completely fake acceleration graph example:

So when is the acceleration greatest to the left and right?