How do you use calculus in the real world?

Answer 1

Calculus is used alot in the real world, a common example is in impact testing for cars. When a car is thrown at a wall, the time it takes to hit the wall and the distance it travelled are known. However if you want to calculate a velocity at ANY point along the line you have to formula an equation and then differentiate it to find out such a thing. Example:

y = velocity m/s

dy/dx = acceleration 0m/s/s

y = x^3 - x^2 + 6

dy/dx = 3x^2 - 2x

So therefore

0 = 3x^2 - 2x

Simplifying:

2x = 3x^2

2/3 = x

Plugging back into the real equation of y = x^3 - x^2 + 6 when x = 2/3

y = 5.85185 m/s