True or False

Calculus Level 4

False True

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展豪張
May 5, 2016

By symmetry $s$ is the reflection of $r$ about the line $y=x$ .
This also meets the property of inverse function.

How is two distinct lines tangent to the same graph at the same point? Unless, they are confounded. Isn't the tangent is a line that intersects the graph at one point, especially here f(x)= 1/x. Through one point, we can draw so many lines, but only one would be tangent to a curve at one point. We can not draw two tangents at the same point A to f(x).

Hana Wehbi - 5 years, 1 month ago

The point A does not belong to the curve ..

Jose Sacramento - 5 years, 1 month ago

That is the definition of a tangent: a line that intersects the curve at one unique point, so A should belong to the curve. The problem states that r and s are tangents to f(x) at A.

Hana Wehbi - 5 years, 1 month ago

@Hana Wehbi – I think there is a mistake in the content of the problem? Am I right?

Hana Wehbi - 5 years, 1 month ago

@Hana Wehbi – Yes you are right.. I am sorry.. I made a correction to the problem.

Jose Sacramento - 5 years, 1 month ago

@Jose Sacramento – No worries ;)

Hana Wehbi - 5 years, 1 month ago

I think the question should have been " tangents to the curve passing through point A" and not "tangent to the curve at point A".

Pranav Rao - 5 years, 1 month ago

@Pranav Rao – I agree with you. The wordings are a little bit confusing.

展豪張 - 5 years, 1 month ago

True or False

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