Question

I NEED HELP PLEASE
let f be the function given by
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

f(x) = square root of (x^4-16x^2)

Answer 1

Well if something is under a square root, are there any restrictions on that number?

Answer 2

no...i don't think so?

Answer 3

Can you take a square root of a negative number?

Answer 4

the square root isn't negative though

Answer 5

Can't x be made so that the square root could be negative?
Say if x is 1, you cant take the square root, because the stuff under the square root is negative

Answer 6

So to find the domain of f, we have to say f(x) >= 0
square root of (x^4-16x^2) >= 0 , take both sides to the power of 2,
x^4-16x^2 > = 0
what values of x make the function zero?

Answer 7

not sure...thats why i need step by step answers

Answer 8

You must have an idea where to start though >>

Answer 9

\[x^4-16x^2 < 0 \]

Answer 10

See. That is illegal because then it will be a negative number under the radical.

Answer 11

So find those illegal numbers and send them to jail and ban them from the domain.

Answer 12

\[x^2(x^2-16)<0\]

Answer 13

x^2 will never be negative but x^2-16 might be.

Answer 14

When would x^2-16 be negative?

Answer 15

Try some numbers. What about 0? If x is 0 would x^2-16 be negative?

Answer 16

It's much easier to help you understand if you actually answer me.