If f(x) and f¹(x) are inverse functions of each other and f(x) = 2x+ 5, what is ƒ˜¹ (8) ?
1 answer:
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Answer:
C) The partial derivatives were not evaluated a the point.
D) The answer is not a linear function.
The correct equation for the tangent plane is or
Step-by-step explanation:
The equation of the tangent plane to a surface given by the function in a given point
can be obtained using:
(1)
where and
are the partial derivatives of
with respect to
and
respectively and evaluated at the point
.
Therefore we need to find two missing inputs in our problem in order to use equation (1). The coordinate and the partial derivatives
and
. For
just evaluating in the given function we obtain
and the partial derivatives are:
Now, substituting in (1)
Notice that until this point, we obtain the same equation as the student, however, we have not evaluated the partial derivatives and therefore this is not the equation of the plane and this is not a linear function because it contains the terms ( and
)
For finding the right equation of the tangent plane, let's substitute the values of the partial derivatives evaluated at the given point:
or