Purchase Solution

Finding the Critical Point and Relative Minimum and Maximum

Not what you're looking for?

Ask Custom Question

Consider the function f(x) = 4kx^(3) - (k^2 - 13)x + 9k, where k is a constant.

(a) Suppose that f has a critical point at x = 1. Find all possible value(s) of k. If there is more than one answer, enter them separated by commas.

Answer: f has a critical point at x = 1 exactly when k = ______

(b) If f has a relative maximum at x = 1, find all possible value(s) of k. If there is more than one answer, enter them separated by commas.

Answer: f has a relative maximum at x = 1 exactly when k=______

(c) If f has a relative minimum at x = 1, find all possible value(s) of k. If there is more than one answer, enter them separated by commas.

Answer: f has a relative minimum at x = 1 exactly when k = _______.

Purchase this Solution
Solution Summary

Solution provides steps necessary to calculate the critical point, the relative minimum and the relative maximum.

Solution Preview

Consider the function f(x) = 4kx^3 - (k^2 - 13)x + 9k, where k is a constant.

(a) Suppose that f has a critical point at x = 1. Find all possible value(s) of k. If there is more than one answer, enter them separated by commas.

We have f^'(x) = 12kx^2 - (k^2 - 13)
Suppose that f ...

Purchase this Solution
Free BrainMass Quizzes
Probability Quiz

Some questions on probability

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

View More Free Quizzes
Related BrainMass Solutions

  • Finding critical points of a function z=f(x,y)

    Find all critical points of the function: f (x,y) = x^3 + y^3 - 4x - 9y + 17 Classify the critical point as a relative minimum, relative maximum, or saddle point using the second derivative test.

  • Finding Maximum and Minimum Values

    516402 Finding Maximum and Minimum Values Questions: A) Find all critical points of f(x)=x^5+5x^4-35x^3 and classify each as a relative minimum, relative maximum or neither one.

  • Functions: Critical Points, Extrema and Saddle Points

    23170 Functions: Critical Points, Extrema and Saddle Points Find the critical points of the given function and classify each as relative minimum, relative maximum, or a saddle point.

  • Maximizing Revenue

    Determine the critical points of the given function and classify each critical point as a relative maximum, a relative minimum, or neither. a. a. (4.5, -32) relative maximum; x = 5 neither; x = 4 neither, b.

  • Finding Critical Numbers; Finding the Extrema in the Interval; etc.

    23111 Finding Critical Numbers; Finding the Extrema in the Interval 1. Find all the critical numbers: . 2. Find all the extrema in the interval [0,2 ] for . 3. Find the absolute maximum and the absolute minimum on the interval (1,4]. 4.

  • Critical Points

    152139 Critical Inflection Point The graph of f(x) = ln(x^2) has a. neither a relative minimum nor a point of inflection at x = 0 b. a relative minimum that is not an inflection point at x = 0 c. a relative maximum that is not an inflection point

  • Derivatives : Maximum and Minimum Values

    when y < 3b, dV/dy <0, and y >3b, dV/dy >0, Using the first derivative test, at the above critical point, the volume is relative minimum. By the uniqueness of the critical number, it must be an absolute minimum.

  • Extreme values

    (b) On the line segment between and , we have So has minimum and has maximum (c) On the line segment between and , it has equation , then So has minimum and maximum (d) At the critical point , has value There, in the

  • Finding relative extrema and inflection points

    keywords: maximum, minimum, local, maxima, minima Please see the attached file for the complete solution. Thanks for using BrainMass.

View More Related Solutions