Question

Please help!!
Let f be the function given by f(x)=sq.rt. of x^4-16x^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) = slope

-1/f'(x) is the normal (the perpendicular slope)

Answer 2

a) The argument of the square root is only negative between -4 and 4, so the domain is
(−∞,−4]∪[4,∞)

b) see attachment
c) evaluate the derivative when x = 5. It is 34/3. so the slope of the normal is -3/34