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Aleksandr [31]
3 years ago
13

I want to make sure i got this right. PLS HELP ASAP I NEED IT CALC 1 one question

Mathematics
1 answer:
IrinaK [193]3 years ago
6 0
\bf f(x)=
\begin{cases}
x^3&x\le 1\\
mx+b&x\ \textgreater \ 1
\end{cases}

now, a function may well be continuous, but it may not be differentiable.

graph wise, differentiability means, a smooth curve, with no abrupt spikes or drops or cuts.

so for this piece-wise to be differentiable, the subfunctions must meet at junctions smoothly, with no abrupt changes, so mx + b, must blend in with x³ smoothly.

now, that can only occur if mx + b has the same slope as x³ at that point where they meet.  The point where they meet is at x = 1, well, let's check what is the slope of x³ at x = 1.

\bf \cfrac{d}{dx}[x^3]\implies \left.  3x^2\cfrac{}{}\right|_{x=1}\implies 3(1)^2\implies 3

therefore "m" for mx+b, must be 3 then.

now, what's the value of x³ at x = 1?  well is just (1)³, which is 1.

so for 3x + b, when x = 1, it must also equals 1 as well, that way it meets x³, thus

3x + b

3(1) + b = 1

b = -2

check the graph below.

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Find the value of the missing coefficient in the factored form of 8f^3-216g^3
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Answer:

The value of the missing coefficient is 12

Step-by-step explanation:

* Lets explain how to factorize the difference of two cubes

- The factorization of the difference of two cubes like a³ - b³, is a

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- The binomial is the cube root of the first term and the second term

∵ The ∛a³ = a and ∛b³ = b

∴ The binomial is (a - b)

- We will find the trinomial from the binomial by square the 1st term

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∴ The trinomial is (a² + ab + b²

∴ The factorization of (a³ - b³) is (a - b)(a² + ab + b²)

* Lets solve the problem

∵ 8f³ - 216g³ is the difference of two cubes

∵ ∛(8f³) = 2f

∵ ∛(216g³) = 6g

∴ The binomial is (2f - 6g)

- Lets make the trinomial

∵ (2f)² = 4f²

∵ (2f)(6g) = 12fg

∵ (6g)² = 36g²

∴ The trinomial = (4f² + 12fg + 36g²)

∴ The factorization of 8f³ - 216g³ = (2f - 6g)(4f² + 12fg + 36g²)

∴ The value of the missing coefficient is 12

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Answer:

9: a^8/c^2

Step-by-step explanation:

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