SOLUTION: Determine an expression for f(x) in which f(x) is cubic, f(x)&#8805; 0 when x &#8804; 2, f(x) < 0 when x > 2, and f(0) = 4.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Determine an expression for f(x) in which f(x) is cubic, f(x)&#8805; 0 when x &#8804; 2, f(x) < 0 when x > 2, and f(0) = 4.       Log On


   

Question 1022005: Determine an expression for f(x) in which f(x) is cubic, f(x)≥ 0 when x ≤ 2, f(x) < 0 when x > 2, and f(0) = 4.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

In order for it to be positive before and negative after x=2, then it must look like this,
f%28x%29=a%28x-2%29%5E3
or else you will have an additional set of directional changes.
So now solve for the constant.
After x=2 the cubic will be positive so the constant needs to be negative.
So,
f%28x%29=-a%28x-2%29%5E3
f%280%29=-a%280-2%29%5E3=4
a=4%2F8
a=1%2F2
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f%28x%29=-%28x-2%29%5E3%2F2
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