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Mathematics
Mathematics
Problem
Explain why the expression
g
′
(
t
)
f
′
(
t
)
\dfrac{g'(t)}{f'(t)}
f
′
(
t
)
g
′
(
t
)
cannot be used to obtain the slope of the tangent at
t
=
t
0
t=t_0
t
=
t
0
if
f
′
(
t
0
)
=
0
f'(t_0)=0
f
′
(
t
0
)
=
0
but
g
′
(
t
0
)
≠
0
g'(t_0)\neq0
g
′
(
t
0
)
=
0
.
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