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3 years ago

Use the graph of f(x) below to estimate the value of f '(3):

Mathematics

2 answers:

Shalnov [3]3 years ago

6 0

Answer:

-5 he was off by one :/

Step-by-step explanation:

klio [65]3 years ago

3 0

Well, looking at the graph, notice, its vertex is at 0,9, and it passes through the points -3,0 and 3,0, so hmm let's use 3,0, to get the equation of f(x)

$\bf ~~~~~~\textit{parabola vertex form}
\\\\
\begin{array}{llll}
\boxed{y=a(x- h)^2+ k}\\\\
x=a(y- k)^2+ h
\end{array}
\qquad\qquad
vertex~~(\stackrel{}{ h},\stackrel{}{ k})\\\\
-------------------------------$

$\bf vertex~(0,9)~
\begin{cases}
h=0\\
k=9
\end{cases}\implies y=a(x-0)^2+9
\\\\\\
\textit{we also know that }
\begin{cases}
x=3\\
y=0
\end{cases}\implies 0=a(3-0)^2+9
\\\\\\
-9=9a\implies \cfrac{-9}{9}=a\implies -1=a\quad thus\quad \boxed{y=-x^2+9}
\\\\\\
\left. \cfrac{dy}{dx}=-2x \right|_{x=3}\implies -6$

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Step-by-step explanation:

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Step-by-step explanation:

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2 years ago

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aleksklad [387]

Answer:

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Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

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In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

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