Question

Show that there are no tangents to the curve y=x+2/(3x+4) with positive slope.

Answer 1

take derivative first, show me the result

Answer 2

10/(3x+4)^2

Answer 3

-2, not 10

Answer 4

oops!

Answer 5

you know the answer now, right?

Answer 6

not really, how does that show there are no tangents? it is because of the negative? @Loser66

Answer 7

It is not "no tangent", it is "no negative tangent"

Answer 8

derivative of a function is tangent line form, right? you get \(\dfrac{-2}{(3x+4)^2}\)
the denominator is always positive (exponent 2), the numerator is always negative
then, the factor is always <0, how can we have a positive slope?

Answer 9

*fraction, not factor. I am sorry

Answer 10

thanks for the explanation! I got it now :) @Loser66