Here's a toughie.

At each point (x,y) on the curve the slope equals the square of the distance between the point and the y-axis; the point (-1,2) is on the curve. Find the equation of this function.

Question

Here's a toughie.

At each point (x,y) on the curve the slope equals the square of the distance between the point and the y-axis; the point (-1,2) is on the curve.  Find the equation of this function.

anonymous · Answer

Knowing that the x-value is the perfect measure for the distance from the y-axis, I came up with$$f'(x)=(\left| x \right|)^2$$ as the eqn for the slope.  But does that make sense...?

anonymous · Answer

isnt that just:
$$y' = x^2 \Rightarrow y = \frac{x^3}{3}$$
or am i over simplifying things <.<

anonymous · Answer

i dont like calculus btw >.<

anonymous · Answer

Just adjust with with Constant
$$2=\frac{1}{3}(-1)^3+C$$
$$y=\frac{1}{3}x^3+\frac{7}{3}$$

anonymous · Answer

Hmm.  I guess throwing in those absolute value bars messed me up.  Thanks all!

anonymous · Answer

We don't need absolute value since x^2 is always positive

anonymous · Answer

y=1x+3