The last is one and the lump of clay one is correct. The law of conversation is that energy can not be created, nor destroyed. This is a perfect example because the apple is not losing any of the matter it had in the beginning.
Slope-intercept form: y = -2x - 1. Convert this to point-slope form:
Find a point on the graph. It's (0, -1), since y = -2(0) - 1 = -1.
Then the point-slope form is
y-(-1) = -2(x - 0)
![y = 2x {}^{2} + e {}^{ - x {}^{4} }](https://tex.z-dn.net/?f=y%20%3D%202x%20%7B%7D%5E%7B2%7D%20%20%2B%20e%20%7B%7D%5E%7B%20-%20x%20%7B%7D%5E%7B4%7D%20%7D%20)
![\frac{dy}{dx} = 4x +( e {}^{ - x {}^{4} } )( - 4x {}^{3} )](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%204x%20%2B%28%20e%20%7B%7D%5E%7B%20-%20x%20%7B%7D%5E%7B4%7D%20%7D%20%29%28%20-%204x%20%7B%7D%5E%7B3%7D%20%29)
![\frac{dy}{dx} = 4x - 4x {}^{3} e { }^{ - x {}^{4} }](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%204x%20-%204x%20%7B%7D%5E%7B3%7D%20e%20%7B%20%7D%5E%7B%20-%20x%20%7B%7D%5E%7B4%7D%20%7D%20)
![\frac{dy}{dx} = 4x(1 - x {}^{2} e {}^{ - x {}^{4} } )](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%204x%281%20-%20x%20%7B%7D%5E%7B2%7D%20e%20%7B%7D%5E%7B%20-%20x%20%7B%7D%5E%7B4%7D%20%7D%20%29)
![\frac{dy}{dx} = 0 \\ 4x = 0 \: \: \: \: \: 1 - x {}^{2} e {}^{ - x {}^{4} } = 0](https://tex.z-dn.net/?f=%20%5Cfrac%7Bdy%7D%7Bdx%7D%20%20%3D%200%20%5C%5C%204x%20%3D%200%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%201%20-%20x%20%7B%7D%5E%7B2%7D%20e%20%7B%7D%5E%7B%20-%20x%20%7B%7D%5E%7B4%7D%20%7D%20%20%3D%200)
![4x = 0 \\ x = 0 \: \: \: \: \: \: y(0) = 0 + e {}^{0} = 1](https://tex.z-dn.net/?f=4x%20%3D%200%20%5C%5C%20x%20%3D%200%20%5C%3A%20%20%20%5C%3A%20%20%5C%3A%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20y%280%29%20%3D%200%20%2B%20e%20%7B%7D%5E%7B0%7D%20%20%3D%201)
<h2>
![\frac{x {}^{2} }{e {}^{x {}^{4} } } = 1 \\ x {}^{2} = e {}^{x {}^{4} } \\ 2ln(x) = x {}^{4} \\ these \: 2 \: functions \: do \: not \: intersect](https://tex.z-dn.net/?f=%20%20%5Cfrac%7Bx%20%7B%7D%5E%7B2%7D%20%7D%7Be%20%7B%7D%5E%7Bx%20%7B%7D%5E%7B4%7D%20%7D%20%7D%20%3D%201%20%5C%5C%20x%20%7B%7D%5E%7B2%7D%20%20%3D%20e%20%7B%7D%5E%7Bx%20%7B%7D%5E%7B4%7D%20%7D%20%20%5C%5C%202ln%28x%29%20%3D%20x%20%7B%7D%5E%7B4%7D%20%20%5C%5C%20these%20%5C%3A%202%20%5C%3A%20functions%20%5C%3A%20do%20%5C%3A%20not%20%5C%3A%20intersect)
</h2><h2>Stationary point ( 0 , 1 )</h2>
<h2 />
The problem is, I don't think that you estimated for letter a, so you can't do letter b.
So you can solve this by drawing a digram. Draw each points and label all checkpoints. Study the drawing as long as you can to understand the situation. The question is asking for too much, so its a slippery slope.