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Let $f(x) = x^3 + 6x^2 + 9x + 3$. (a) Sketch the curve $y = f(x)$ in big parts. (b) How many different real rots does the equation $f(x) = 0$ have? (c) For which values on a does the equation $f(x) = a$ have exactly two real rots?

Answer on (a)

Firstly, I diferentied the function and put the derivative equal to zero. From that I got extreme values.

Secondly I put the value of x to zero to see where the curve cross the y-axis.

How do I get the points where the curve cross the x-axis algrebracially? What is enough of sketching this graph in big parts?

Answer on (b)

I can see from the extreme points that there are tre points on the x-axis, but how can if there are real roots or not ?

Answer on (a)

I dont know what they mean?

I am asking here since I dont have the solutions but only the key. Any help is appreciated.

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    what have you done? – 2017-01-09
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    On b) the roots you found on the axis are prob real. And on c) try to calculate dy/dx and find where the discriminant > 0 – 2017-01-09
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    here you can find all about the cubic https://en.wikipedia.org/wiki/Cubic_function – 2017-01-09
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    On (a), I cant get the values algebracially of the points where it crosses the x-axis. How should I do ? When I insert the equation in wolfram alpha it says that there are only two real roots and the third they say it is imaginary point – 2017-01-09

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