Part 2/7:
Let's consider a function ( f(x) ) represented graphically as a curve. If we choose a point ( a ) on this curve, we can find the tangent line at that point—often referred to as the linear approximation ( L(x) ). The equation of this tangent line can be expressed as follows:
[ L(x) = f'(a)(x - a) + f(a) ]
Where:
( f'(a) ) represents the derivative of ( f ) at point ( a ), indicating the slope of the tangent line.
( f(a) ) is the value of the function at point ( a ).
This equation allows us to estimate values of ( f(x) ) for ( x ) values that are close to ( a ).