Mathematics

Problem

Geometrically, the value of

\displaystyle\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}

, if it exists, gives a) the slope of the normal to

y=f(x)

(x,\,f(x))

b) the slope of the secant through

(x, f(x))

and

(x+h,f(x+h))

c) the slope of the tangent to

y=f(x)

(x,\,f(x))

d) the instantaneous rate of change of

x

with respect to

y

(x,\,f(x))