Answer:
K(x) = [tex]\frac{-10}{[1 + (-10x)^2]^{\frac{3}{2} } }[/tex] ( curvature function)
Step-by-step explanation:
considering the Given function
F(x) = [tex]-5x^2[/tex]
first Determine the value of F'(x)
F'(x) = [tex]\frac{d(-5x^2)}{dy}[/tex]
F'(x) = -10x
next we Determine the value of F"(x)
F"(x) = [tex]\frac{d(-10x)}{dy}[/tex]
F" (x) = -10
To find the curvature function we have to insert the values above into the given formula
K(x) [tex]= \frac{|f"(x)|}{[1 +( f'(x)^2)]^{\frac{3}{2} } }[/tex]
K(x) = [tex]\frac{-10}{[1 + (-10x)^2]^{\frac{3}{2} } }[/tex] ( curvature function)
