Analyzing Functions Explained by Our Experts

Given the function $f (x) = \frac{1}{12} x^{4} + \frac{1}{6} x^{3} - 3 x^{2} - 2 x + 1$ how do you find any points of inflection and determine where the curve is concave up or down?

Arianna Villegas 2022-03-24

For what values of x is $f (x) = \frac{- 2 x^{2}}{x - 1}$ concave or convex?

fellesturduj 2022-03-15

What is the largest interval on which the function is concave down for $f (x) = 5 \sin (x) + {(\sin (x))}^{2}$ over the interval $[- \frac{π}{3}, 2 \frac{π}{3}]$ ?

Isabelle Diaz 2022-03-15

What is the parametric equation of an ellipse?

Nikhil Holt 2022-03-14

What x values is the function concave down if
$f (x) = 15 x^{\frac{2}{3}} + 5 x$ ?

Olivia Mcgrath 2022-02-15

Sketch the graph of each of the following rational functions. Explicitly state the values asked for below and show how you determined those values.
a) the equations of any horizontal asymptotes
b) the equations of any vertical asymptotes
c) any non-permissible values as a coordinate (other than asymptotes)
$y = \frac{1}{x - 3} + 2$

Jennifer Beasley 2022-02-15

The derivative of a certain continuous and differentiable function is given by:
$y^{'} = 3 - x^{2} - 22 - x + 9$
Analyze the function and create a sketch of the original if the only zeros are at $x = 0$ and $x = 3$ .

Janiyah Higgins 2022-02-15

Find the inverse function of $f^{- 1}$
$f (x) = \frac{x - 2}{3 x + 5}$

auskunftsgkp 2022-02-14

Analyze the function.
$f (x) = {\begin{array}{ccc} \frac{1}{2} x + 13 & if & x < 8 \\ \sqrt{8 x} + 9 & if & x \geq 8 \end{array}$
Is f(x) diferential at $x = 8 ?$ Explain why or why not in your Discussion post.

Amiya Arellano 2022-02-14

Find the function f given that the slope of the tangent line at any point (x, f(x)) is f '(x) and that the graph of f passes through the given point. $f' (x) = 4 (2 x - 9)^{3} 5, 11 / 2$

Randy Mejia 2022-02-13

Analyze the function.
$f (x) = {\begin{array}{ccc} \frac{1}{2} x + 12 & if & x < 2 \\ \sqrt{2 x} + 11 & if & x \geq 2 \end{array}$
A.) Is f(x) continuous at $x = 2$ ?
B.) Is f(x) differentiable at $x = 2$ ?

Caitlin Esparza 2022-02-12

Find the critical points of the following functions. Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, local minimum, or saddle point. Confirm your results using a graphing utility.
$f (x, y_{=} {(4 x - 1)}^{2} + {(2 y + 4)}^{2} + 1$

Olivia Mcgrath 2022-02-03

Analyzing critical points Find the critical points of the following functions.Use the Second Derivative Test to
determine (if possible) whether each critical point corresponds to a local maximum, a local minimum,or a
saddle point. If the Second Derivative Test is inconclusive,determine the behavior of the function at the critical
points.
$f (x, y) = \frac{λ}{1 + x^{2} + y^{2}}$

urlacainnxp 2022-01-31

A researcher is analyzing regional differences in family size. She has information on the number of children for samples of families from four different regions. Which statistical test should she conduct?

poveli1e 2022-01-31

68. Analyzing a Line A line is represented by the equation $a x + b y = 4$ .
(a) When is the line parallel to the x-axis?

veceriraby 2022-01-31

The primary measures of central tendency and dispersion should be described.
Why are they crucial in data analysis?

mairie0708zl 2022-01-31

Suppose your manager indicates that for a normally distributed data set you are analyzing, your company wants data points between $z = - 0.6 z = - 0.6$ and $z = 0.6 z = 0.6$ standard deviations of the mean (or within 0.6 standard deviations of the mean). What percent of the data points will fall in that range?
Answer: percent (Enter a number between 0 and 100, not 0 and 1 and round to 2 decimal places)

poveli1e 2022-01-30

Which of the following statements is not true?
Multiple Choice
A statistic is a single measure (usually numerical) that is calculated from a sample.
For day-to-day business data analysis, most firms rely on a large staff of expert statisticians.
A statistical test may be significant yet have no practical importance.
Statistics is the science of collecting, organizing, analyzing, interpreting, and presenting data.

Vilharjevw7 2022-01-29

What are the real-life applications of Statistics in Business and Economics? Briefly explain at least three examples.

2022-01-17

Justify that you have found the requested point by analyzing an appropriate derivative. $x = 2 \sin t$ ,
$y = \cos t$ ,
$0 \leq t \leq π$
Rightmost point.

As you are analyzing function completely ap problems, you will need clear examples that will contain detailed answers to your questions. Since there will be more than equations alone, the most important is to provide analysis. The same relates to analyzing function packet answers that can be either answered based on instructions (as in many replies below) as well as generated by various software. Reading through both examples will help you to see how calculus implements functions and what aspects of analysis must be provided to receive complete answers.

Calculus 1

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