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IrinaVladis [17]
3 years ago
15

\[f(x)=\sqrt{x ^4-16x ^{2}}\]

Mathematics
1 answer:
marusya05 [52]3 years ago
4 0
f ( x ) =  \sqrt{ x^{4} -16 x^{2} }
a ) The domain:
x^4 - 16 x² ≥ 0
x² ( x² - 16 ) ≥ 0
x² - 16 ≥ 0
x² ≥ 16
x ∈ ( - ∞, - 4 ] ∪ [ 4 , + ∞ )
b ) f ` ( x ) = \frac{1}{2 \sqrt{x ^{4}-16 x^{2}  } } *  ( x^{4}-16 x^{2} )` =
= ( 2 x³ - 16 x ) / √(x^4 - 16 x²)
c ) The slope of the tangent line at x = 5:
f ` ( 5 ) = ( 2 * 125 - 16 * 5 ) / √ ( 625 - 400 ) = 170 / 15 = 34 / 3
The slope of the line normal to the graph at x = 5:
m = - 3 / 34 
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Read 2 more answers
For a party, the family bought 24 pizzas for $12.50 each and 36 bottles of soda for $1.20 each. How much did the family spend on
xxTIMURxx [149]

Answer:

1) The amount the family spent on pizza is $300

2) The amount the family spent on soda is $43.2

3) The amount the family spent in all is $343.2

Step-by-step explanation:

The number of pizzas bought by the family = 24

The price of each pizza = $12.50

The number of bottles of soda the family bought = 36

The price of each bottles of soda = $1.20

1) The amount the family spent on pizza = 24 × $12.50 = $300

2) The amount the family spent on soda = 36 × $1.20 = $43.2

3) The amount the family spent in all = The amount the family spent on pizza + The amount the family spent on soda

∴ The amount the family spent on soda = $300 +$43.2 = $343.2.

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Answer:

Step-by-step explanation:

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