find the radius of curvature for y= x^2-4x^3-18x^2 at origan(0,0)
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The radius of curvature for y = x^2 - 4x^3 - 18x^2 at the origin (0,0) is 27/17.
What is radius of curvature?
The radius of curvature is a property of a curve at a specific point on the curve. It is defined as the radius of the circle that best fits the curve at that point.
To find the radius of curvature (R) for the given function y = x^2 - 4x^3 - 18x^2 at the origin (0,0), we need to use the formula:
R = [(1 + y'^2)^(3/2)] / |y"|
where y' and y" are the first and second derivatives of y with respect to x, respectively.
First, we find the first derivative of y:
y' = 2x - 12x^2 - 36x
Next, we find the second derivative of y:
y" = 2 - 24x - 36
At the origin (0,0), x = 0. Therefore, we have:
y'(0) = 0 - 0 - 0 = 0
y"(0) = 2 - 0 - 36 = -34
Substituting these values into the formula for R, we get:
R = [(1 + 0^2)^(3/2)] / |-34| = 27/17
Therefore, the radius of curvature for y = x^2 - 4x^3 - 18x^2 at the origin (0,0) is 27/17.
To know more about radius of curvature and given link below -
https://brainly.in/question/1891492
https://brainly.in/question/820654
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