Please help! What is the local minimum value of the function g(x)=x^4-5x^2+4? (Round answer to the nearest hundredth)

Question

anonymous · Answer

first differentiate g(x)

anonymous · Answer

equate this to xero and solve for x

jdoe0001 · Answer

the minimum of that parabola equation will be at the vertex
you can find the vertex of a parabola equation like so $\bf ax^2+bx+c$    at $\bf \left(-\cfrac{b}{2a}\quad ,\quad  c-\cfrac{b^2}{4a}\right)$

jdoe0001 · Answer

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anonymous · Answer

but with the equation x^4-5x^2+4 how do i do -b/2a?

anonymous · Answer

@galli when I put in 0 for the x's I got 4. Would the minimum value be 4?

campbell_st · Answer

well it is interesting as the curve has 2 miniumums... 

so you will need calculus... 

find the 1st derivative and set to to zero

then solve for x

anonymous · Answer

@campbell_st to find the 1st derivative do I put a 0 for all of the x's in the function? If so, i did that and I got 4

campbell_st · Answer

just go back a step, what did you get for the 1st derivative..?

campbell_st · Answer

you may also need the 2nd derivative to test the stationary points found in the 1st derivative

anonymous · Answer

what exactly is a derivative?

campbell_st · Answer

ok... so you haven't done calculus... 

so I'll assume its an algebra question... 

would that be right?

jdoe0001 · Answer

ohh smokes... didn't notice it was a quartic

anonymous · Answer

this is pre-calculus but math is definitely my worst subject so yeah..

campbell_st · Answer

well its ok@jdoe, it is a quartic reducible to a quadratic... which allow the zeros to be found easily

anonymous · Answer

yeah im just really confused with this question overall /:

campbell_st · Answer

so if you haven't used differentiation then its just a more difficult question to answer

jdoe0001 · Answer

are you supposed to graph it?

anonymous · Answer

no i just need the number of minimum value