Question

For what values of c does the curve have maximum and minimum values?
F(x) 4x^3+cx^2+4x

Answer 1

v

Answer 2

solve F ' (x) = 0

Answer 3

@perl how would that work with c? Because it's the anti-discriminant. I have 12x^2+2cx+4=0

Answer 4

@perl yeah that's what I had so would you do the quadratic, take the value that is greater than 0, and then solve it like a regular min/max by plugging back into the original equation?

Answer 5

yes that sounds correct.

Answer 6

$$
\Large {

f(x) = 4x^3 +cx^2 + 4x \\
f ' (x) = 12x^2 + 2cx + 4 \\
\\ \therefore\\ 12x^2 + 2cx + 4 = 0
\\ \therefore\\ 6x^2 + cx + 2 = 0

\\ \therefore\\ c^2 -4(6)(2)\geq 0
\\ \therefore\\ c^2 \geq 48

}
$$