# Math

How many x-intercepts and how many local extrema does the polynomial P(x)= x(sqrt)3-4x have?

How many x-intercepts and how many local extrema does the polynomial Q(x)=x^3-4x have?

and If a>0, how many x-intercepts and how many local extrema does each of the polynomials P(x)=x^3-ax and Q(x)=x^3+ax? Explain your answer.

1. 👍 0
2. 👎 0
3. 👁 116
1. If P(x) = x^2-4x, then since
P(x) = x(x-4), it has two x-intercepts.

Q(x) = x(x^2-4) = x(x-2)(x+2)
so Q has 3 roots.

x^2-ax = x(x^2-a) = x(x-√a)(x+√a)
so there are 3 roots
With 3 roots, there must be 2 extrema.

x^2+ax = x(x^2+a)
since a>0, x^2+a can never be zero, so there is only 1 x-intercept, at x=0.
There are no extrema, since the derivative is never zero.

1. 👍 0
2. 👎 0
posted by Steve

## Similar Questions

1. ### Calculus

Graph the following function. Find and state the domain, intercepts, asymptotes, intervals of increase and decrease, local extrema, concavity, and inflections points. F(x)=(x+1)/(square root(x^2+1)) I got so far... Domain:

asked by Devin on October 20, 2012
2. ### Calculus

Find a second degree polynomial f(x) (of the form ax2+bx−4) that has a local extrema at (−1/2,−9/2).

asked by M on October 11, 2018
3. ### Math

I have researched what a local extrema is and every definition is weird or worded to where i do not understand it. Can anyone explain what local extrema is.

asked by Confused on December 11, 2017
4. ### calcus

determine domain, intercepts, asymptotes, intervals of increase and decrease, and concavity, and to locate any local extrema and point of inflection.

asked by Anonymous on March 26, 2011

You helped me with this question and this is what I got but my Professor says that each x and y intercept needs to have a coordinate. Where did I go wrong?? Can you help me? x^2+y^2+4x+2y-20=0 x^2+4x+4+y^2-2y+1=20+4+1

6. ### math

Find the x-intercepts of the polynomial y = x^2 - 4x + 3 I'm not sure how to approach this -- do I first factor it and then my x intercepts are (#, 0)? So, for example, factored would be (x - 3)(x - 1) I set those equal to 0 so my

asked by Carly on April 30, 2019
7. ### math

Given the function f(x)=x^4−6x^2 a.) Find all values of x where local extrema points occur b.)find all values of x where inflection points occur c.) find all local extrema of f(x) d.) find all global extrema of f(x) over the

asked by Ryan on November 26, 2012
8. ### Algebra

Below is the graph of a polynomial function f with real coefficients. Use the graph to answer the following questions about f. All local extrema of f are shown in the graph. I really need help with this one but I can't post the

asked by Rachal on February 4, 2011
9. ### Calculus

Score for Question 2: ___ of 40 points) For the polynomial (x)=x^5-5x^4+12x^3-24x^2+32x-16 , answer the following questions. Show all of your work. How many zeros does the function have over the set of complex numbers? What is the

asked by Kat on January 17, 2018
10. ### Calculus

Given the function: f(x) = x^2 + 1 / x^2 - 9 a)find y and x intercepts b) find the first derivative c) find any critical values d) find any local(relative) extrema e) find second derivative f) discuss the concavity g) find any

asked by Gabby on April 28, 2013

More Similar Questions