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September 15, 2014

September 15, 2014

Posted by **Victoria** on Saturday, May 10, 2008 at 4:55pm.

(a) Find the value of the real constant, a. Find the function f(x).

(b) Find the stationary points of the function, then specify the intervals on which the function is increasing and those on which the function is decreasing

(c) Find the intervals on which f(x) is concave up, and those on which it is concave down.

- Maths -
**drwls**, Saturday, May 10, 2008 at 6:33pm1. Integrate the gradient function

ax^2-12x + 9 to get f(x), except for an arbitary constant C.

f(x) = (ax^3)/3 -6x^2 +9x + C

If (2,-3) is an inflection point, the second derivative of f(x) must be zero there.

2ax -12 = 0 @ x=2

ax = 6

a = 3

Use f(x) and the statement that y=-3 at x=2 to solve for C

(b) Stationary points occur where the derivative of f(x) is zero.

(c) f(x) is concave down where f''(x) < 0 and concave up where f''(x) >0

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