Question

can somebody help me with this question?
2: let f be the function given by :
f(x)=((x^4)-(16x^2))^(1/2)

a) Find the domain of f.
b) Find f '(x)
c) Find the slope of the line normal to the graph of f at x = 5

Answer 1

\[f(x)=\sqrt{x^4-16x^2}\]
\[f'(x)=\frac{4x^3-32x}{2\sqrt{x^4-16x^2}}\] then some algebra

Answer 2

domain is
\[x^4-16x^2\geq 0\]
\[x^2(x^2-16)\geq 0\]
\[(-\infty, -4)\cup\{0\}\cup (4,\infty)\]

Answer 3

algebra for derivative gives
\[\frac{4x^3-32x}{2x\sqrt{x^2-16}}\]
\[\frac{2x^2-16}{\sqrt{x^2-16}}\]

Answer 4

ty

Answer 5

um.. excuse me but im still a lil confused a bit bout part c can u explain it to me again