Help with inverse of derivative function

[Hazy001]

f(x) =

3x^3 + 3x^2+ 2x + 1
,a = 3

formal is

Homework is due tonight and this is the only problem i can't solve

Your suppose to
3=

3x^3 + 3x^2 + 2x + 1
, solve for xThe find the derivative of y=

3x^3 + 3x^2 + 2x + 1
, then plug x into that and put it under 1.

 

[Mark44]

f(x) =

3x^3 + 3x^2+ 2x + 1
,a = 3

What does a represent? I infer from your work below that you are taking it to mean the point (x₀, a) on the graph of f.

formal is

Homework is due tonight and this is the only problem i can't solve

Your suppose to
3=

3x^3 + 3x^2 + 2x + 1
, solve for xThe find the derivative of y=

3x^3 + 3x^2 + 2x + 1
, then plug x into that and put it under 1.

Assuming that your interpretation is the correct one, start with this equation:
$3 = \sqrt{3x^3 + 3x^2 + 2x + 1}$, and then square both sides. The resulting equation is not the easiest to solve, but it does have one real solution.

 

[Hazy001]

Yes that is it but sadly i cannot solve it

 

[Ray Vickson]

Yes that is it but sadly i cannot solve it

You want to solve $p(x) = 0$, where $p(x) = 3 x^3 + 3 x^2 + 2x - 8$.
(i)One thing to try is the "rational root theorem"; see, eg.,
http://en.wikipedia.org/wiki/Rational_root_theorem .
(ii) Alternatively, plot the graph of $y = p(x)$ over some $x$-range, to see roughly where a root lies; that will suggest a factor of $p(x)$, which you can then verify exactly. (iii) If you are still desperate you can always submit the problem to an on-line solver, such as Wolfram Alpha.