The answer of all of this is 18 because 18.1 months so if you do the math you get 18-7x+20^2
Answer: Depends on the function but to figure this out you look for the growth factor in the equation is greater than 1
Answer:
(a) f'(1)=-4
(b) y+4x-4=0
Step-by-step explanation:
<u>Tangent Line of a Function</u>
Given f(x) a real differentiable function in x=a, the slope of the tangent line of the function in x=a is given by f'(x=a). Where f' is the first derivative of f.
We are given
![y=x-x^5](https://tex.z-dn.net/?f=y%3Dx-x%5E5)
The derivative is
![y'=1-5x^4](https://tex.z-dn.net/?f=y%27%3D1-5x%5E4)
(a) The slope of the tangent line at (1,0) is
![f'(1)=1-5\cdot 1^4=-4](https://tex.z-dn.net/?f=f%27%281%29%3D1-5%5Ccdot%201%5E4%3D-4)
![f'(1)=-4](https://tex.z-dn.net/?f=f%27%281%29%3D-4)
(b) The equation of the tangent line can be found with the general formula of the line:
![y-y_o=m(x-x_o)](https://tex.z-dn.net/?f=y-y_o%3Dm%28x-x_o%29)
Where m is the slope and the point (xo,yo) belongs to the line. We have m=-4, xo=1, yo=0, thus
![y-0=-4(x-1)](https://tex.z-dn.net/?f=y-0%3D-4%28x-1%29)
Or, equivalently
![y+4x-4=0](https://tex.z-dn.net/?f=y%2B4x-4%3D0)
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