Question

Find the -coordinates of the points where the graph of the function

f(x)=(2x^2-7)^3

has a horizontal tangent line. (Hint: There are 3 of them.)

Answer 1

the function f(x) = (2x^2-7)^3 is a polynomial... this does not have a horizontal tangent. Is the function as written correct?

Answer 2

ya thats exactly how it is written in the problem.

Answer 3

ok i just plugged in zero for my answer and it was correct, so anytime i see a standard polynomial i know that the answer cannot exist with a problem of this type? or how can i tell?

Answer 4

polynomials don't have asymptotes. rational functions of polynomials (among others) do. they look like fractions of polynomials... example... f(x)=(x^3+x-5)/(x^3+3x-2).

Answer 5

for horizontal asymptotes, all you need to check is the degree of the polynomial on the numerator and denominator. If the degree on the numerator is less than the degree of the denominator, then y=0 is your horizontal asymptote.

Answer 6

oh ok easy enough

Answer 7

horizontal tangent line!!! sorry, I misread the question. I thought you were looking for horizontal asymptotes. I'll get on this...

Answer 8

OK, I got it... find the horizonta tangents for f(x)=(2x^2-7)^3. You'll need the derivative which is f'(x)=12x(2x^2-7)^2. So looking at the factors, you'll have a horizontal tangent (f'(x)=0) at x = 0, sqrt(7/2), -sqrt(7/2). three of them, like you said