calculus

This was a multiple choice question asking which of the following is an equation of the line tangent to the graph of f(x)=x^4+2x^2 at the point where f'(x)=1?

and the answer is y=x-0.122, but I don't understand why.

I tried to take the derivative of f(x) and got 4x^3+4x = 1 and solved for x, but I am not getting the answer. What am I doing wrong and how do I solve this?
Thanks!

you did nothing wrong, you are just faced with an equation very hard to solve.

4x^3 + 4x - 1 =0

I got x = .2367329 by a method called Newton's Method, which is sort of hard to explain in this forum.
substituting back in the original I go y=.1152257

so we have the point (.2367,.1152) and slope of 1
When used in y=mx+b I indeed got

y = x - .1215, they rounded it off to 3 decimals.

I don't know if you are in highschool or college, so I don't know what kind of tools you have to solve equations of that type.

how did you get b=.1215 though?

y=mx+b
.2367 = .1152 + b
b=.2367-.1152
b=.1215


The equation is not difficult to solve at all! You only need to know is a simple trick:

4x^3+4x - 1 = 0 --->

x^3 = -x + 1/4 (1)

The trick is to compare this with the equation for (a+b)^3, which you can write as:

(a+b)^3 = 3 a b(a+b) + a^3 + b^3 (2)

If you compare (2) to (1), you see that if you can find values for a and b such that

3 a b = -1 and a^3 + b^3 = 1/4 (3)

then a + b is a solution to the equation! But finding the numbers a and b such that (3) is satisfied amounts to solving a quadratic equation:

3 a b = -1 --->

a^3 b^3 = -1/27

So, if we put A = a^3 and B = b^3, then we have:

A B = -1/27

A + B = 1/4

A solution is:

A = 1/8 + sqrt[1/64 + 1/27]

B = 1/8 - sqrt[1/64 + 1/27]

And a solution for x is:

x = a + b = A^(1/3) + B^(1/3) =

[sqrt(1/64 + 1/27) + 1/8]^(1/3) -
[sqrt(1/64 + 1/27) - 1/8]^(1/3)

which gives the same result as Reiny gave above.

  1. 👍 0
  2. 👎 0
  3. 👁 144
  1. qckfu zoasubw ceyriow abke nyod ixkyj zqurci

    1. 👍 0
    2. 👎 0
  2. (1/64)^x=Sqrt1/8

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. Statistical concept 68-95-99.7

    1. A student taking a midterm exam in Ancient History comes to two questions pertaining to a lecture that he missed, and so he decides to take a random guess on both questions. One question is true-false and the other is multiple

    asked by Surpreet Pororsha on April 21, 2016
  2. Stat HW for.

    1. A student taking a midterm exam in Ancient History comes to two questions pertaining to a lecture that he missed, and so he decides to take a random guess on both questions. One question is true-false and the other is multiple

    asked by Jen N. on April 21, 2016
  3. Math

    a 10 question multiple choice test has 4 possible answer for each question. A student selects at least 6 correct answers. Find probability of this event: (multiple choice) A) .118 B) .995 C) .068 D) .571

    asked by Matt Borchelt on December 13, 2011
  4. English for john browm

    Let me give you something on "multiple-choice" items that may help you to guess better. Many teachers prepare multiple-choice tests because they are easy to mark and offer the student the advantage of actually seeing what the

    asked by SraJMcGin on May 7, 2009
  5. Math

    Each day Julia's math Teacher gives class a warm up qs. It's true/false 20% of the times and multiple choice 80% . Julia gets 70% on true false correct and 90% on multiple choice correct. Julia answered today's question correctly.

    asked by Jason on April 15, 2015
  6. Math

    A history quiz consists of 60 points and contains questions that ate either true/false or multiple-choice. If a true/false question is worth 3 points and a multiple-choice question is worth 8 points, and the quiz has at least one

    asked by Suzan on January 23, 2018
  7. Career

    Please check my answers. Thank you! The amount of goods and services that people want to buy. Producers Consumers Supply Demand* Question 2 (Multiple Choice Worth 10 points) (02.08 LC) Knowledge and tools that enable us to do new

    asked by Anonymous on September 23, 2016
  8. Math

    what is the solution to the system of equations? 5x + 4y = 8 x - 2y = 10 (not multiple choice) my answer: (-5, -1) What are the missing values? (coincident) 4x + 5y = 8 8x + ____ y = _____ (Not multiple choice) Im not sure how to

    asked by Anonymous on November 19, 2014
  9. English

    Question 4 (multiple choice) A system that does not allow a worker to fail will not _________________ . be sued allow a worker to succeed fail as a system C? Question 5 (multiple choice) An apprentice is a worker who

    asked by Bri on November 20, 2017
  10. character education

    ____________ is necessary to develop positive social relationships. Charm Respect Talent B? Question 18 (true/false) An individual's identity is rarely influenced by his or her peers and friends. True False False? Question 19

    asked by Bri on December 1, 2017
  11. Math (Algebra)

    Gretchen and Ezia received equal scores on a test made up of multiple choice questions and an essay. Gretchen got 18 multiple choice questions correct and received 19 points for her essay. Ezia got 15 multiple choice questions

    asked by Anonymous on October 6, 2015

More Similar Questions