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nikitadnepr [17]
3 years ago
13

Find the indicated quantities for y equals f (x )equals 3 x squared. ​(A) Simplify StartFraction f (3 plus Upper Delta x )minus

f (3 )Over Upper Delta x EndFraction . ​(B) What does the quantity in part ​(A) approach as Upper Deltax approaches​ 0?
Mathematics
1 answer:
torisob [31]3 years ago
5 0

Answer:

6x

Step-by-step explanation:

Given that a function f(x) is given as

y=f(x) = 3x^2

A) f(x+ \Delta x) = 3((x+ \Delta x)^2=3(x^2+2x \Delta x+\Delta x^2)\\f(x) = 3x^2\\f(x+ \Delta x) -f(x) = 6x  \Delta x +\Delta x^2

Now divide by delta x

\frac{f(x+ \Delta x) -f(x)}{\Delta x}\\=6x+\Delta x

B) When delta x tends to 0, this becomes

6x

(NOte: This is the derivative of f(x))

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