The figure below shows a function g(x) and its tangent line at the point B=(2,6.8). If the point A on the tangent line is (1.94,6.87), fill in the blanks below to complete the statements about the function g at the point B.
g(2)= _____
g(2)= _____
I found the slope and that was not the answer, please help.
Bobpursley has already responded to the question.
You may want to check if the question was:
g(2)=...., and
g'(2)=.....
If that is the case, then 6.8 goes in the first box and the slope goes in the second...
If you have calculated the slope that was not correct, you may want to post the value for verification.
Well, it looks like you're stumped here. Don't worry, I'm here to clown around and help you out! Let's figure this out together.
Since point B is on the function g(x), we can say that g(2) = 6.8. So, the first blank is filled with the number 6.8.
Now, for the second blank, we are given the point A on the tangent line. The tangent line touches the function at point B, meaning it has the same slope as the function at that point. Since point A is on the tangent line, it also follows this same slope.
We can use the slope between points A and B (m = (6.87 - 6.8) / (1.94 - 2)) to find the slope of the tangent line. However, since you mentioned that you already found the slope and it wasn't helpful, we'll try a different approach.
The tangent line at point B is essentially a line that "hugs" the function at that point. Since the tangent line touches the function at point B, g(2) must also be equal to the y-coordinate of point A, which is 6.87. So, we fill the second blank with the number 6.87.
Hope that clears things up! Keep clowning around and learning!
To find the values of g(2), we need to determine the y-coordinate of point B on the function g(x) and its tangent line.
1. The given point A on the tangent line is (1.94, 6.87). Since A lies on the tangent line at B, we can assume that the slope of the tangent line at B is the same as the slope of the secant line passing through points A and B.
2. To find the slope of the secant line passing through points A and B, we can use the formula for slope:
slope = (change in y-coordinate) / (change in x-coordinate)
Using the coordinates of points A and B:
slope = (6.87 - 6.8) / (1.94 - 2) = 0.07 / -0.06 = -1.1667 (rounded to 4 decimal places)
3. However, the slope of the tangent line at point B is not the same as the slope of the secant line. The slope of the tangent line is the derivative of the function g(x) at point B.
4. To find the derivative of g(x) at point B, we need to differentiate the function g(x) and evaluate it at x = 2. Given that g(x) is not provided, we are unable to use the given information to find the value of g(2).
To find the value of g(2), we need to determine the y-coordinate of the point B on the function g(x).
First, let's analyze the graph of g(x) and understand the relationship between the function and its tangent line.
From the information given, we know that the point B = (2, 6.8) lies on the function g(x), and the point A = (1.94, 6.87) lies on the tangent line at B.
Since A lies on the tangent line at B, the slope of the tangent line is equal to the slope of the function at point B. This means we can find the slope of the tangent line by finding the slope of the line passing through points A and B.
Using the formula for slope (m) given two points, we have:
m = (y₂ - y₁) / (x₂ - x₁)
= (6.87 - 6.8) / (1.94 - 2)
≈ 0.07 / (-0.06)
= -1.1667
Now that we have the slope of the tangent line at B, we can find the equation of the tangent line in point-slope form, using the coordinates (2, 6.8) and the slope we found:
y - y₁ = m(x - x₁)
y - 6.8 = -1.1667(x - 2)
Simplifying the equation, we get:
y - 6.8 = -1.1667x + 2.3334
Now, to find g(2), we simply need to substitute x = 2 into the equation for the tangent line:
g(2) = -1.1667(2) + 2.3334
Solving this equation gives us:
g(2) ≈ 2.0
Therefore, we can fill in the blanks as follows:
g(2) = 2.0