Question

let f(x)=x^4 + ax^2, what is a if f has a local min at x=5? what is the value of a if f has a point of inflection at x=2?

Answer 1

\[\frac{ dy }{ dx }=4x^3+2ax\]
\[\frac{ d^2y }{ dx^2 }=12x^2+2a\]
At S.P's (Stationary points)
\[\frac{ dy }{ dx }=0\]
\[4x^3+2ax=0\]
\[2x(2x^2+a)=0\]
\[x=0\]
or
\[x^2=-\frac{a}{2}\]
When y''>0, T.P(Turning Point) is minimum.
\[12x^2+2a>0\]
\[12(5)^2+2a>0\]
\[300+2a>0\]
\[2a>-300\]
\[a>-150\]
At I.P's (Inflexion/Inflection Points)
y''=0
\[12x^2+2a=0\]
\[6x^2+2a=0\]
\[6(2)^2+2a=0\]
\[2a=-24\]
\[a=-12\]

Answer 2

@Goaliess1

Answer 3

@Goaliess1 You there?

Answer 4

yea, I re posted it to see how others went about solving it , thanks by the way.

Answer 5

Never repost.

Answer 6

No matter what reason, do not repost.

Answer 7

There's a bump button for a reason.

Answer 8

oh ok. won't happen again.