if mathematically derivatives are the opposite of integrals, conceptually how is the area under a curve opposite to the slope of a tangent line?

Question

if mathematically derivatives are the opposite of integrals, conceptually how is the area under a curve opposite to the slope of a tangent line?

In: 332

Answer 1

Both are characteristics of the same function. They are related, but they are not the same thing.

For example, if you are on a trip, it is possible to plot the velocity versus the time (how fast you are going at each moment).

The area under the curve is how far you traveled. The slope of the curve is how fast you are accelerating at that moment.

Different information/characteristics of the same thing.