Find the function

Calculus Level 4

For a certain cubic function, f ( x ) f(x) , I know that:

  • At x = 3 x=3 , the tangent is the x x -axis

  • f ( 0 ) = 0 f(0)=0

  • f ′ ( 0 ) > 0 f'(0)>0

What is this function?

x 3 − 6 x 2 + 9 x x^3-6x^2+9x Not enough information x 3 + 6 x 2 − 9 x x^3+6x^2-9x x 3 − 6 x 2 − 9 x x^3-6x^2-9x − x 3 + 6 x 2 + 9 x -x^3+6x^2+9x − x 3 − 6 x 2 − 9 x -x^3-6x^2-9x x 3 + 6 x 2 + 9 x x^3+6x^2+9x − x 3 − 6 x 2 + 9 x -x^3-6x^2+9x

Jihoon Kang by Jihoon Kang , 24, United Kingdom

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1 solution

Prakhar Gupta
Apr 14, 2015

The given information determines the 3 3 roots of f ( x ) f(x) .

Also we are able to determine the sign of slope at x = 0 x=0 .

With this information we can say that f ( x ) = k x ( x − 3 ) 2 f(x) = kx(x-3)^{2} But we have no information with which we can determine the value of k k .

Hence information is not enough to uniquely determine f ( x ) f(x) .

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice approach. I did it by considering general cubic polynomial. Your approach is definitely time saving.

Abhishek Sharma - 6 years, 2 months ago

Very good . Perfect explanation

Jihoon Kang - 6 years, 1 month ago

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Thank you.

Prakhar Gupta - 6 years, 1 month ago

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