MHB Application of Differentiation Problem - Need help

[Lyle1]

Hi,
I have a problem of which I do not know where to start or how to go about solving it.

- The graph of the function equation y=f(x) is shown, where f(x) is a cubic polynomial. The graph cuts through the origin, touches the x-axis at (3,0) and passes through (4,4).

a) - Prove that f(x) = x³-6x²+9x

b) - Use calculus to find the coordinates of the local maximum of the graphAny help would be appreciated. Thanks in advance (:

 

[tkhunny]

Hi,
I have a problem of which I do not know where to start or how to go about solving it.

- The graph of the function equation y=f(x) is shown, where f(x) is a cubic polynomial. The graph cuts through the origin, touches the x-axis at (3,0) and passes through (4,4).

a) - Prove that f(x) = x³-6x²+9x

b) - Use calculus to find the coordinates of the local maximum of the graphAny help would be appreciated. Thanks in advance (:

You have three points, two zeros, and a y-intercept. Are you SURE you don't know where to start?

 

[Greg]

a) As 0 is a zero of f(x) and there is a double root at 3, the equation of f(x) is x(x - 3)$^2$. When expanded this is equivalent to the equation you are given. Whether this is rigorous enough to be considered proof will be up to you.

What difficulty are you having with part b)?