# calc

posted by .

one more question!!

what values of c deos the polynomial f(x) = x^4 + cx^3 + x^2 have two inflection points? one inflection point?

At the inflection point, the slope of the curve is zero.

Find the dervative of f(x) and set it equal to zero. For certain values of c, there will be one or two values for x.

isn't it the second derivative

I apologize. My initial response was completely wrong.

You are correct. The second derivative will equal zero at inflection points. Not the first.

okay so i got this

2nd der = 12x^2 + 6cx + 2 = 0

i get stuck here

You will find that for certain values of c, x can have one or two values.

okay, so trial and error?

At an inflection point the second derivative is zero. The second derivative is:

f''(x) = 12x^2 + 6cx + 2

If this quadratic function is to have only one zero, it must be of the form:

A (x-B)^2

The coefficient of x^2 is A but you know that this must be 12, so A = 12. The constant term is A B^2 = 12 B^2, which must be 2, so you can deduce that that B = +/- squareroot[1/6]. The term linear in x is
-2ABx = -/+ 24 squareroot[1/6] x

This must be 6cx, so you find that

c = -/+ 4 squareroot[1/6]

So, you see, this problem can again be solved using differentiation and factorization. These sort of problems are a simple and boring. Do you want to see a more interesting application of these techniques?

No. Setup your quadratic formula. The formula includes a plus-minus sign, which means there are zero, one or two solutions for each quadratic.

In other words, solve for x.

At an inflection point the second derivative is zero. The second derivative is:

f''(x) = 12x^2 + 6cx + 2

If this quadratic function is to have only one zero, it must be of the form:

A (x-B)^2

The coefficient of x^2 is A but you know that this must be 12, so A = 12. The constant term is A B^2 = 12 B^2, which must be 2, so you can deduce that that B = +/- squareroot[1/6]. The term linear in x is
-2ABx = -/+ 24 squareroot[1/6] x

This must be 6cx, so you find that

c = -/+ 4 squareroot[1/6]

what is BOZOOOOOOOOOOOOOOOOOOOOOOOOOO

## Similar Questions

1. ### Math - exponential

How many inflection points does f(x) = xe^(x^(-2)) have?
2. ### calculus

f(x)= x^3/x^2-16 defined on the interval [-19,16]. Enter points, such as inflection points in ascending order, i.e. smallest x values first. Enter intervals in ascending order also. What are F(x) TWO vertical asympototes?
3. ### calc.

I'm having a lot of trouble with this problem: Sketch the graph and show all local extrema and inflections. f(x)= (x^(1/3)) ((x^2)-175) I graphed the function on my graphing calculator and found the shape. I also found the first derivative: …
4. ### calculus

Find all relative extrema and points of inflection of the function: f(x) = sin (x/2) 0 =< x =< 4pi =< is supposed to be less than or equal to. I can find the extrema, but the points of inflection has me stumped. The inflection …
5. ### Calculus

The number of people who donated to a certain organization between 1975 and 1992 can be modeled by the equation D(t)=-10.61t^(3)+208.808t^(2)-168.202t+9775.234 donors, where t is the number of years after 1975. Find the inflection …
6. ### calculus

Use a graph of f(x) = 3 e^{-8 x^2} to estimate the x-values of any critical points and inflection points of f(x). critical points x= Inflection points x= Next, use derivatives to find the x-values of any critical points and inflection …
7. ### Calculus

If f(x) is a continuous function with f"(x)=-5x^2(2x-1)^2(3x+1)^3 , find the set of values for x for which f(x) has an inflection point. A. {0,-1/3,1/2} B. {-1/3,1/2} C. {-1/3} D. {1/2} E. No inflection points
8. ### Calculus

For what values of a and b is (2, 2.5) is an inflection point of the curve x^2 y + ax + by = 0 ?
9. ### College Pre-Calc

a.)Determine the location of the turning points for the cubic y=x^3-3x^2+2x+10. What are the maximum and minimum values for this function?
10. ### Math Calc

Find the x-coordinates of any relative extrema and inflection point(s) for the function f(x) = 3x(1/3) + 6x(4/3). You must justify your answer using an analysis of f '(x) and f "(x) I got -1/8 for a minimum point and 1/4 for inflection …

More Similar Questions