A curve has equation y = f(x).(a) Write an expression for the slope of the secant line through the points P(4, f(4)) and Q(x, f(x)).(b) Write an expression for the slope of the tangent line at P.

Answer 1

Secant line:

[ f(x) - f(4)] / (x-4) = dQ(x) <--- difference quotient

Tangent line:

lim dQ as x-->4