Using derivatives, it is found that the best estimate of f '(2) based on this table of values is of 10.
The rate of change <u>from x = 0 to x = 2</u> is given by:
From <u>x = 2 to x = 4</u>, it is given by:
The average of these rates is:
Hence, the best estimate of f '(2) based on this table of values is of 10.
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Answer:
is the required equation.
Therefore, the second option is true.
Step-by-step explanation:
We know that the slope-intercept form of the line equation of a linear function is given by
where m is the slope and b is the y-intercept
Taking two points (0, -2) and (1, 0) from the table to determine the slope using the formula
substituting the point (0, -2) and the slope m=2 in the slope-intercept form to determine the y-intercept i.e. 'b'.
Now, substituting the values of m=2 and b=-2 in the slope-intercept form to determine the equation of a linear function
Thus, is the required equation.
Therefore, the second option is true.