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Values of x and g(x) are given in the table below. x 3.1 3.6 4.1 4.6 5.1 5.6 6.1 6.6 g(x) 3.8 4.8 5.4 5.8 6.4 7.8 9.4 11.4 for what value of x in the table is g '(x) closest to 3?

Respuesta :

alybsinger
I'm assuming that each number is in correspondence with a number of the other variable in terms of order.

What you want to do is look at each value of g(x) and see which number is closest to 3, then which ever value of x was plugged in for that function is your answer.

So the value of g(x) that is closest to 3 is 3.8 which I'm assuming that would mean the value of x would be 3.1 because it also comes first in the order you gave
xero099

There are two options in which [tex]g'(x)[/tex] is closest to 3: 1) [tex]x = 5.1[/tex], 2) [tex]x = 5.6[/tex]. Hence, we conclude that a value of [tex]x[/tex] between 5.1 and 5.6 has [tex]g'(x) = 3[/tex].

In this question, we shall use the concept of derivative, which is related to the concept of secant line, relationship that is presented below:

[tex]g'(x_{i}) \approx \frac{g(x_{i+1})-g(x_{i})}{x_{i+1}-x_{i}}[/tex] (1)

Where:

  • [tex]g'(x_{i})[/tex] - First derivative of the function evaluated at [tex]x_{i}[/tex].
  • [tex]g(x_{i})[/tex] - Function evaluated at [tex]x_{i}[/tex].
  • [tex]g(x_{i+1})[/tex] - Function evaluated at [tex]x_{i+1}[/tex].

Now we proceed to estimate the derivatives:

[tex]g'(5.1) \approx \frac{7.8-6.4}{5.6-5.1}[/tex]

[tex]g'(5.1) \approx 2.8[/tex]

[tex]g'(5.6) \approx \frac{9.4-7.8}{6.1-5.6}[/tex]

[tex]g(5.6) \approx 3.2[/tex]

There are two options in which [tex]g'(x)[/tex] is closest to 3: 1) [tex]x = 5.1[/tex], 2) [tex]x = 5.6[/tex]. Hence, we conclude that a value of [tex]x[/tex] between 5.1 and 5.6 has [tex]g'(x) = 3[/tex].

We kindly invite to see this question on derivatives: https://brainly.com/question/2788760

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