The difference quotient as h > O is the instantaneous rate of change. True or false? True False Question 7 5 pts A linear equation is characterized by one slope (with one value that is the same regardless of delta x and delta y). For non-linear equations the derivative provides one equation describing how output changes as input changes: this equation is the same regardless of where along the domain of the function we inquire as to how out changes as input changes. 80, one equation describes how output changes with changes in input, but different values are produced by this equation depending on the choice of input to the function. True or false? True False Question 8 5 pts Let C be the total cost of manufacturing a certain good with the cost a function of quantity produced (q) and assume that C(q) = 3q2. The derivative of C with respect to q is given by which of these DQs (with h --> 0)? a. 6q b. 6q - 3h2 c.6q-3h=6q The derivative of a function measures how the value of the function value (output value) changes with respect to a change in its argument (input value). True/False r"' True False _ The equation for the slope of an equation is: Ay/ Ax; Ay can be expressed as f(x + Ax) f(x) where Ax indicates a change in the value of x. True/False. D Question 11 5 pts In mathematics a variable is a placeholder for the value of a clearly dened and delineated feature of a system, process or entity which can be measured. True/False ' True ' False Question 12 5 pts In ecology the Logistic population growth model is an equation in which the growth of a biological population depends on both the existing population size and the amount of available resources (carrying capacity). Letting P represent population size, and t denote time, this model is formalized by the equation: dP/dt = rP(1 P/K), where the constant r species the growth rate and K is the carrying capacity. The previous equation is the derivative of population with respect to time, that is, how population changes over time. True/False ' True ' False