Based on the graph of f(x), the value of f '(3) is approximately 3.
Based on the graph of f(x) below, the value of f '(3) is approximately 3.
graph of f(x) with a tangent line drawn at x=3 and the slope of the tangent line labeled as 3.
To estimate the value of f '(3), we can approximate the slope of the tangent line to the graph at x=3. The slope of the tangent line represents the instantaneous rate of change of the function at that point, which is equal to the derivative of the function at that point.
To approximate the slope of the tangent line, we can choose two points on the line and use the rise-over-run formula. In this case, we can choose the points (2,2) and (4,4), which are two points on the tangent line that are close to x=3. The slope of the tangent line is then:
(4-2)/(4-2) = 2/2 = 1
Therefore, we can estimate that the value of f '(3) is approximately 1.
Note that this is just an estimate, since we are approximating the slope of the tangent line. If we were to calculate the exact derivative of f(x) at x=3, we might get a slightly different answer. However, this estimate is close enough for most practical purposes.