Please help me. Dont judge.

Mathematics

2 answers:

crimeas [40]3 years ago

7 0

The answer is A. Because to get rid of the five you have to do reverse property so if it's subtraction you'd change it to adding to get rid of the 5

tia_tia [17]3 years ago

6 0

It would be A because u need to add 5

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Determine the values of the constants B and C so that the function given below is differentiable.

laila [671]

For the function to be differentiable, its derivative has to exist everywhere, which means the derivative itself must be continuous. Differentiating gives

$f'(x)=\begin{cases}24x^2&\text{for }x1\end{cases}$

The question mark is a placeholder, and if the derivative is to be continuous, then the question mark will have the same value as the limit as $x\to1$ from either side.

$\displaystyle\lim_{x\to1^-}f'(x)=\lim_{x\to1}24x^2=24$
$\displaystyle\lim_{x\to1^+}f'(x)=\lim_{x\to1}B=B$

So the derivative will be continuous as long as $B=24$

For the function to be differentiable everywhere, we need to require that $f(x)$ is itself continuous, which means the following limits should be the same:

$\displaystyle\lim_{x\to1^-}f(x)=\lim_{x\to1}8x^3=8$
$\displaystyle\lim_{x\to1^+}f(x)=\lim_{x\to1}Bx+C=24+C$

$24+C=8\implies C=-16$

So, the function should be

$f(x)=\begin{cases}8x^3&\text{for }x\le1\\24x-16&\text{for }x>1\end{cases}$

with derivative

$f'(x)=\begin{cases}24x^2&\text{for }x$

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4 years ago

Based on the graph of the line below, which describes the relationship between the value of the y-intercept and the

stepan [7]

Answer:

y intercept = 3

$m = \frac{1}{3}$ --- slope