Question

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 this formula to find the curvature function of the following curve. ​f(x)=−5x2 The curvature function is κ​(x)=nothing.

Answer 1

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)