Thread: i need some quick help here...

1. i need some quick help here...

A cubic polynomial with a local maximum at x = 1, a local minimum at x = 3, a y-intercept of 6, and an x3 term whose coefficient is 1.

ok, so how the flip do i do this bad johnny...thanks for any help..

mathaction

2. Originally Posted by mathaction
A cubic polynomial with a local maximum at x = 1, a local minimum at x = 3, a y-intercept of 6, and an x3 term whose coefficient is 1.

ok, so how the flip do i do this bad johnny...thanks for any help..

mathaction
Ok...i assume you want to find the cubic.

Let the general form of the cubic be $f(x) = x^3 + ax^2 + bx + c$

we know that $c = 6$ since this is the y-intercept.

so we have: $f(x) = x^3 + ax^2 + bx + 6$

since the local max is at x = 1, it means $f'(1) = 0$ and $f''(1) < 0$

since the local min is at x = 3, it means $f'(3) = 0$ and $f''(3) > 0$

can you continue? (you may not need the second derivative, i just gave you extra information for your general edification)