Difference between f(x) and f'(x)? what is meant by slope of a tangent line? diff between line & tangent line?

Answer 1

In Algebra, you learned about the slope of lines. In calculus, this concept is extended to non-linear relations. If f(x) is such a relation, rather than having a constant slope, its slope is f'(x), which can changed in numerical value for different values of x. The line with the numerical value of slope at point x,y on f(x) is a tangent line. It is a line, however, for any other point (x,y) on f(x), you would get an altogether different tangent line.

Answer 2

f(x) and f'(x) are functions
slope of tangent line =f ' (x)
slope=tan(angle) in positive direction

tangent line and f have one common point.

y=mx+n is a line