Inflection points are places on a curve where the concavity changes. And so to find an inflection point, we need to not only find where the second derivative is 0, but we need to verify that the sign on the second derivative also changes. This is similar to how a slope of 0 does not...
function. If {eq}\displaystyle f'(x) {/eq} tells us about the slope of the function {eq}\displaystyle y = f(x) {/eq} then the second derivative {eq}\displaystyle f ' ' (x) {/eq} tells us about the rate of change of the slope of the function, which is nothin...
The Ct value can be determined as the intersection of a line tangent to the growth curve at the maximum of the second derivative with a baseline of the growth curve. Such a Ct value is usable for sigmoidal curves and parabolic curves, and can provide linear calibration curves to achieve ...
Many interpretations and developments of the Financial Instability Hypothesis (FIH) rely on aggregate leverage ratio indicators to proxy non-financial firm
The conformation of α-crystallin was quantitatively estimated from the vibrational analysis of amide I band achieved by second-derivative analysis, Fourier self-deconvolution and curve fitting program. The results indicate that all the α-crystallin samples did not show a large different composition in...
To achieve this goal, it is necessary to determine the absolute concentrations of oxygenated and deoxygenated haemoglobin. Others have used the second derivative of the water spectrum in the near infrared region to calculate absolute deoxy-haemoglobin concentra- tion [3], but the calculation is ...
Using implicit differentiation, find the derivative of the equation. 3x^2 y^2 + 4y^5 + 8x^2 y^3 + xy = 5Find y'' by implicit differentiation given that 3x^2 + y^2 = 9Consider the curve 3x^2 + 7y^2 = 9. Find y' and y" by implicit dif...
You can use the constraint equations to eliminate x and y, leaving you with just a function of t, which is z = f(2cos(t), 3sin(t)). Then differentiate and set the result to zero to find critical points. Then use the second derivative test to determine whether each critical point ...
Critical points are the points where slope of the curve is zero. At these points function stops increasing or decreasing. Hence maximum or minimum value of the function occur at these critical point only. By finding the sign of second derivative of the fun...
The graph of the derivative f of a continuous function f is shown. Determine at what intervals is f concave upward or downward? Concavity: The second derivative of a function can be used to determine its concavity. This is because the...