Example Problem 1: How to Find Intervals of Upward Concavity For a Function and its Graph by Using the Second Derivative of the Function. Determine where the functionf(x)=12x3−6x2+19is concave up. Step 1:Compute the second derivative of...
If the graph of a function is given, we can determine the function's concavity or convexity, by looking where the tangent line to the graph lie with respect to the graph. If the tangent line to the graph is above the graph, the function is concave, and if the tangent line is below ...
While the presence of invasive green iguanas and tegu lizards in Florida are attributed to the pet trade, other non-native species have made their way to the state through international trade practices. One example is the Cuban tree frog, which was thought to make its way to Florida via carg...
So, now we can resubstitute these y-values values back into our first equation to find the corresponding x-values. If x=y212 and y=0, then x=0 and z=f(0,0)=0 If x=y212 and y=6, then x=3 and z=f(3,6)=−54 If x=y212 and y=−6, then x=3 and z=f(3,−6...
Concave functions are very useful in maximization problems(like profit maximization), because all you have to do to find the solution is to find where the “peak” of the function is. Definition of a Concave Function A concave function can be defined directly in terms ofconvex functions. They...
By accepting optional cookies, you consent to the processing of your personal data - including transfers to third parties. Some third parties are outside of the European Economic Area, with varying standards of data protection. See our privacy policy for more information on the use of your perso...
Consider the function f(x) = 3x^2 – 6x + 2. We will use the first derivative test to determine if the function is increasing or decreasing. Find the first derivative of the function: f'(x) = 6x – 6. Simplify the derived expression: f'(x) = 6(x – 1). ...
Find ways to convey your message by using images in place of words. Your design and copy should work together as friends, and the more you can communicate visually, the quicker your customers will become interested in the value you’re providing. Align Product Design With Visual Brand If you...
The conversion of the pea’s natural sugar to starch begins immediately after harvest. Some cooks say the greatest lag time between picking and serving peas should be no more than 12 hours. If you serve properly stored peas within a day or two of harvest, you should still find them a tre...
How to Find Intercepts Intersection of Two Lines How to Enter Data into a List TI89 Optimization Problems Quadratic Formula Related Rates Relation vs Function Second Derivatives (Test, Finding) Sum of a Convergent Geometric Series Symbols and Equations (How to Read Them) Vertical Tangents Calculus...