Question

If the tangent line to the curve :
y = x^3 - 3x^2 makes an obtuse angle with the positive x-axis. then :

Answer 1

\[x \in ....\]

Answer 2

what type of answer do you want not direct? not steps?

Answer 3

but you said not steps was it a typo?

Answer 4

a) [0,2] b) ]0,2[ c) Z- [0,2] d) Z - ]0,2[
Looking for steps.

Answer 5

the question itself is sort of ends with then? what

Answer 6

If the tangent line to the curve :
y = x^3 - 3x^2 makes an obtuse angle with the positive x - axis then x∈....
a) [0,2] b) ]0,2[ c) Z- [0,2] d) Z - ]0,2[

Answer 7

well looking at the plot (0,1) would be my answer

Answer 8

i plotted the curve and looked at the tangent line ---wait for another reply maybe
they will see it different

Answer 9

i think you need to plot the curve, and then draw the tangent line in a few times. you will see when it makes an obtuse angle, as opposed to an acute angle, with the x direction....

Answer 10

Isn't there any solution without plotting it and even if so plot it and tell me which answer you think is right ( I got the final answer ).

Answer 11

the tangent line only points downwards between 0 < x < 2. at all other times it points up (makes an acute angle with x axis).

https://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E3+-+3+x%5E2

Answer 12

Right the answer is ]0, 2[ but I want a solution without plotting it.

Answer 13

I got idea, how about using maxima and mimima and check where it's decreasing.

Answer 14

dy/dx = 3x^2 - 6x
x = 0 x= 2
in crease Z- [0,2] decrease ]0,2[
I got it.

Answer 15

Do you agree with this solution ?

Answer 16

Just to be sure, I would sketch the graph.
but "obtuse angle" means negative slope. so solve
3x^2 - 6x < 0
3x(x-2) < 0

we know x >=0 so 3x is positive, i.e. x>0
(x =0 gives zero slope, which means the line does not intersect the x-axis)
thus to get a negative product we require
x-2 < 2
x <2
and
0 < x < 2