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goblinko [34]
3 years ago
10

f(x) = square root ( x^4 -16x^2) 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 .
Mathematics
1 answer:
Bond [772]3 years ago
8 0
A ) The domain:
x^{4} -16 x^{2}  \geq 0 \\  x^{2} ( x^{2} -16) \geq 0 \\  x^{2} -16 \geq 0 \\  x^{2}  \geq 16
x ≤ -4  and x≥ 4  or:  x ∈ ( - ∞ , - 4 ) ∪ ( 4  , + ∞ )
b ) f ` ( x ) = \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}  } }
c ) The slope of the line normal to the graph at x = 5
m = -1 / f `(x)
f ` ( x ) = \frac{10(25-8)}{ \sqrt{625-400} }=  \frac{10*17}{15} = \frac{34}{3}
m = - 3/34 

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