a ) The domain:
[tex] x^{4} -16 x^{2} \geq 0 \\ x^{2} ( x^{2} -16) \geq 0 \\ x^{2} -16 \geq 0 \\ x^{2} \geq 16[/tex]
x ≤ -4 and x≥ 4 or: x ∈ ( - ∞ , - 4 ) ∪ ( 4 , + ∞ )
b ) f ` ( x ) = [tex] \frac{1}{2 \sqrt{ x^{4} -16 x^{2} } } *( 4 x^{3} - 32 x ) = \\ = \frac{2x( x^{2} -8)}{ \sqrt{ x^{4}-16 x^{2} } } [/tex]
c ) The slope of the line normal to the graph at x = 5
m = -1 / f `(x)
f ` ( x ) = [tex] \frac{10(25-8)}{ \sqrt{625-400} }= \frac{10*17}{15} = \frac{34}{3} [/tex]
m = - 3/34
