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MyaMya12
27.09.2020 •
Mathematics
shown above is the graph of a differentiable function F along with the line tangent to the graph of F at X=3. what is the value of f’3
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Ответ:
Tangent lines are lines that touches a curve at a point, without running over the curve.
The value of f'(3) is -1/2
From the figure, the line tangent to the graph passes through (5,3) and (1,5)
Next, we calculate the slope of the line using:
So, we have:
Simplify
Rewrite as:
The line also passes through (3,4) and (1,5)
So, the slope of the line is:
So, we have:
Rewrite as:
The calculated slope is -1/2
This means that:
Substitute![\mathbf{m = -\frac{1}{2}}](/tpl/images/0781/1260/04b95.png)
Hence, the value of f'(3) is -1/2
Read more about tangent lines at:
link
Ответ:
Option (A)
Step-by-step explanation:
Function 'f' given in the graph is differentiable with a tangent at x = 3.
Since, slope of the function = value of the differentiated function at a point
Tangent at a point x = 3 is passing through two points (3, 4) and (1, 5).
Slope of the function passing through
and
is,
Slope =![\frac{y_2-y_1}{x_2-x_1}](/tpl/images/0781/1260/f6758.png)
=![\frac{5-4}{1-3}](/tpl/images/0781/1260/17707.png)
=![-\frac{1}{2}](/tpl/images/0781/1260/3e56c.png)
Therefore, value of f'(3) will be equal to![-\frac{1}{2}](/tpl/images/0781/1260/3e56c.png)
Option (A) will be the answer.
Ответ:
We need choices if you want to get things done
Step-by-step explanation: