We are asked to estimate the derivative of a function from a graph.
The way we will estimate is calculating the slope of the secant line between two points in the graph of the function f. Let us illustrate with a draw the process
The first thing to do is find two points on the graph and find the equation of the line that pass through them
Inspection of the graph we find that the points
[tex](7.4,5)\text{ and }(7.5,4.6)[/tex]
Therefore, the slope can be calculated using the formula
[tex]\frac{y_2-y_1}{x_2-x_1}=\frac{4.6-5}{7.5-7.4}=-\frac{0.4}{0.1}=-4[/tex]
Therefore, an estimate for the derivative of the function f, at the instant t=7.4 is -4 $/lb
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