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slamgirl [31]
4 years ago
8

The formula κ​(x)= f′′(x) 1+f′(x)23/2 expresses the curvature of a​ twice-differentiable plane curve as a function of x. Use thi

s formula to find the curvature function of the following curve. ​f(x)=−5x2 The curvature function is κ​(x)=nothing.
Mathematics
1 answer:
Katyanochek1 [597]4 years ago
6 0

Answer:

K(x) =  \frac{-10}{[1 + (-10x)^2]^{\frac{3}{2} } }    ( curvature function)

Step-by-step explanation:

considering the Given function

F(x) = -5x^2

first Determine the value of F'(x)

F'(x) = \frac{d(-5x^2)}{dy}

F'(x) = -10x

next we Determine the value of F"(x)

F"(x) = \frac{d(-10x)}{dy}

F" (x) = -10

To find the curvature function we have to insert the values above into the given formula

K(x)  = \frac{|f"(x)|}{[1 +( f'(x)^2)]^{\frac{3}{2} } }

 K(x) =  \frac{-10}{[1 + (-10x)^2]^{\frac{3}{2} } }    ( curvature function)

       

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