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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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3 years ago
There are two numbers. The first number minus the second number is 15. One-third of the sum of the numbers is one quarter of the
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Answer:

So the numbers are 12 and -3.

Step-by-step explanation:

In order to solve this problem we will attribute variables to the numbers, the first one will be "x" and the second one will be "y". From the first sentence we know that the subtraction of the two numbers is equal to 15, so we have:

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2 years ago
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