2. Assume f(t) is a function for which points along the t-axis are measured in hours (hr for short) and function values of f are measured in Coulombs (Cfor short). Let a and b be two real numbers that are not equal.A. Consider two points (a, ƒ(a)) and (b, ƒ(b)) along the graph of function f. The slope of the secant line through these points is measured in units ofC/hr. Explain.B. If f is a differentiable function, it follows from Part A that function values of ƒ' (t) are measured in C/hr. Explain.C. Consider two points (a, ƒ' (a)) and (b, ƒ' (b)) along the graph of ƒ' (t). The slope of the secant line through these points is measured in units ofC/hr². Explain.

Given that ft is a function for which points along the t-axis are measured in hours and function values of f are measured in Coulombs C. We have to write the explanation for the given units.Given that ft is a function for which points along the t-axis are measured in hours and function values of f are measured in Coulombs C. Slope between any two points on the function is change in function value divided by change in input values, the units are measured by function units/input units. A) The two points a, fa and b, fb along the graph of f. Slope of the secant line is defined by change in function value that are measured in Coulombs C divided by change in input value that are measured in hours. Thus, the units are measured by unit change in function/ units change in input i.e., C/hr. Therefore, the points are measured in units C/hr.B) Suppose f is differentiable function. f't is the slope of the tangent line at any time t The first derivative is the rate of change of the function at time t Here, slope of the tangent line is defined by change in function value that are measured in Coulombs C divided by change in input value that are measured in hours at the time t. Thus, the units are measured by unit change in function/ units change in input i.e., C/hr. Therefore, the points are measured in units C/hr. C) The two points a, f'a and b, f'b along the graph of f'. Slope of the secant line of the derivative function tells us the rate of change of the rate of change of the original function. Thus, the units are measured by unit change in function/ unit change in input per unit change in input. Therefore, the points are measured in units C/hr2.