Differentiation Flashcards
The derivative of a function measures …
the sensitivity of change of a dependent variable (y) in response to the change in the independent variable (x).
The derivative of a function of a single variable at a chosen input value is …
the slope of the tangent line to the graph of the function at that point.
The tangent line is …
a straight line which passes through a point on a curve and which just touches the curve at this point;
the best linear approximation of the function near the input value.
Elasticity is the measurement of …
how responsive an economic variable is to a change in another.
Optimization problem is …
the problem of finding the best solution from all feasible solutions.
Stationary points are…
Stationary points (critical points, turning points, extrema) are the points where the tangent of the graph is horizontal and so has zero slope.
The slope (gradient) of the line is …
the change in y divided by the correspondent change in x as you move between any two points on the line.
we read f’(a) as …
f dashed of a
Differentiation is the process …
or operation of determining the first derivative of a function.
First-order derivative is …
the rate of change of a function with respect to its independent variable.
Second-order derivative is …
the derivative of the first-order derivative;
the expression obtained when the original function, y=f(x), is differentiated twice in succession.
Average revenue is …
total revenue per unit of output.
Marginal revenue is …
the extra revenue gained by selling 1 more unit of a good: MR=d(TR)/dQ.
Marginal cost is …
the cost of producing 1 more unit of output: MC=d(TC)/dQ.
Marginal propensity to consume (MPC) is …
the fraction of a rise in national income which goes on consumption: MPC=dC/dY.
Marginal propensity to save (MPS) is …
the fraction of a rise in national income which goes on savings: MPS=dS/dY.
Optimization is …
the determination of the optimal (usually stationary) points of a function.
Maximum (local) point is …
a point on a curve which has the highest function value in comparison with other values in its neighbourhood;
at such a point the first-order derivative is zero and the second-order-derivative is either zero or negative.
Minimum (local) point is …
a point on a curve which has the lowest function value in comparison with other values in its neighbourhood;
at such a point the first-order derivative is zero and the second-order-derivative is either zero or positive.
Stationary point of inflection is …
a stationary point that is neither a maximum nor a minimum;
at such a point both the first- abd second-order derivatives are zero.
