Determinar una expresión para obtener la pendiente de la recta tangente en cualquier
punto a la gráfica:
a) f(x)= x5
b=f(x+h,f(x+h))
f
(
x+h
)
−f(x)
x+h−x=
(
x+h
)
5−x5
h=x5+5x4h+10 x3h2+10 x2h3+5x h4+h5−x5
h
h(5x5+5x4+10 x3h+10 x2h2+5x h3+h4)
h
=
5x4+10 x3h+10 x2h2+5x h3+h4, h ≠ 0
mtan¿x¿¿lim
h−0
5x4+10 x3h+10 x2h2+5x h3+h4
b) f(x)= x6
(
x+h
)
6−x6
x+h−x=x6+6x5h+15 x4h2+20 x3h3+15 x2h4+6x h5+h6−x6
h
=
h(6x5+15 x4h+20 x3h2+15 x2h3+6x h4+h5)
h=6x5+15 x4h+20 x3h2+15 x2h3+6x h4+h5, h ≠ 0
mtan(x)lim
h−0
6x5+15 x4h+20 x3h2+15 x2h3+6x h4+h5