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ollegr [7]
3 years ago
12

How do you find the derivative of a graph

Advanced Placement (AP)
1 answer:
sesenic [268]3 years ago
4 0

Answer:

Choose a point on the graph to find the value of the derivative at. Draw a straight line tangent to the curve of the graph at this point. Take the slope of this line to find the value of the derivative at your chosen point on the graph.

Explanation:

The derivative measures the steepness of the graph of a function at some particular point on the graph. Thus, the derivative is a slope.

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In the Dominican Republic in August, the distribution of daily high temperature is approximately normal with mean 86 degrees Fah
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Answer:

  • <u><em>The standard deviation of the distribution is 1.5ºF.</em></u>

Explanation:

The known 68-95-99.7 rule, the empirical rule, states that, in a normal distribution 68% of the data are within one standard deviation from the mean, 95% of the data are within two standard deviations from the mean, and 99.7% are within three standard deviations:

  • 68% ⇒ mean ± 1 standard deviation
  • 95% ⇒ mean ± 2 standard deviations
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Hence, for the<em> approximately normal distribution of the daily high temperatures</em>,<em> with mean 86º</em>, and a range of <em>83ºF to 89ºF</em> for <em>95% of the data,</em> you can write:

  • 86ºF ± 2 SD ⇒ 86ºF - 2 SD = 83ºF, and

  • 86ºF ± 2 SD ⇒  86ºF + 2SD = 89 ºF

Both equations will lead to the same result:

  • 86ºF - 2 SD  = 83ºF ⇒ 2 SD = 86ºF - 83ºF = 3ºF

         SD = 3ºF / 2 = 1.5ºF

Also:

  • 86ºF + 2SD = 89ºF ⇒ 2 SD = 89ºF - 86ºF = 3ºF

         SD = 3ºF / 2 = 1.5ºF

Therefore, the standard deviation of the distribution is 1.5ºF.

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