![f(x)=(1-x^2)^{\frac{2}{3}}\implies \cfrac{df}{dx}=\cfrac{2}{3}(1-x^2)^{-\frac{1}{3}}\implies \cfrac{df}{dx}=\cfrac{2}{3\sqrt[3]{1-x^2}}](https://tex.z-dn.net/?f=f%28x%29%3D%281-x%5E2%29%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%5Cimplies%20%5Ccfrac%7Bdf%7D%7Bdx%7D%3D%5Ccfrac%7B2%7D%7B3%7D%281-x%5E2%29%5E%7B-%5Cfrac%7B1%7D%7B3%7D%7D%5Cimplies%20%5Ccfrac%7Bdf%7D%7Bdx%7D%3D%5Ccfrac%7B2%7D%7B3%5Csqrt%5B3%5D%7B1-x%5E2%7D%7D)
when it comes to a rational expression, we can get critical points from, zeroing the derivative "and" from zeroing the denominator alone, however the denominator provides critical valid points that are either "asymptotic" or "cuspics", namely that the function is not differentiable or not a "smooth line" at such spot.
if we get the critical points from the denominator on this one, we get x = ±1, both of which are cuspics. Check the picture below.
If you are looking for the equation, then it would be y = -x+3
This is the same as y = -1x+3 which is in slope intercept form y = mx+b
m = -1 = slope
b = 3 = y intercept
If you want to graph this, then plot the points (0,3) and (1,2). Then draw a straight line through them both. Extend the line in both directions as much as possible.
The new coordinates of A'B'C' creates a triangle that is larger than ABC.
<h3>Transformation</h3>
Transformation is the movement of a point from its initial location to a new location. Types of transformation are <em>translation, reflection, rotation and dilation.</em>
If a point A(x, y) is dilated by a scale factor k, the new point is at A'(kx, ky).
Given that:
- Triangle ABC has the following coordinates: A(4 , 5), B(5 , 3), and C(2 , 3)
If it is dilated by a scale factor of 3, the new point is at:
- A'(12, 15), B'(15, 9) and C'(6, 9)
Therefore the new coordinates of A'B'C' creates a triangle that is larger than ABC.
Find out more on dilation at: brainly.com/question/10253650
Answer:
y=2x+1, assuming my change in the reported data was correct.
Step-by-step explanation:
The data for x had one more entry than the values for y. I removed the second "0" so that the x and y points line up, as shown in the attached image. The data indicate a straight line, with a slope of 2 (y increases by 2 for every x increase of 1). The y-intercept is 1, as per the first data point (0,1).
