Calculus stuff

I ve started studying calculus again..The last time i did this, there were many questions and i backed out..Now i am able to understand many things and hence i ll share some things here..

1) Differetiation is all about slopes..Slopes of tangents to curves..Now i had always wondered as to why we need to worry about curves and their slopes..After studying many topics with these, now i realize that we can model almost anything using curves(equations)..ie mathematics is like a programming language. We need to represent real-world problems using some notations..eg..suppose we know(from experiments and observations) that pixel intensity(in images) depends on two factors(say x and y)..we can assume a linear dependence and say pixel_intensity=m*x + n*y..thus as u can see we have an equation of a line now..

now, slope=(change in y)/(change in x)..ie if we get the slope we can get a relation, of how 'y' changes w.r.t 'x'

Entire differentiation circles around this..it s really amazing..