Question

what is the local minimum value of the function g(x)=x^4-5x^2+4

Answer 1

you first have to find \[g \prime (x)\] then once you have found that set g(x) to zero then solve for the x value

Answer 2

how would i find g(x)?

Answer 3

have you been shown the power rule or limit for finding the derivative ?

Answer 4

no

Answer 5

ah look i will show you a fast and easy way to derive this equation :) its call the "power rule"
basicly all you do is move the expontent down to the coefficeient and subtract 1 from the power i.e
\[\frac{d}{dx}x^n= nx^{n-1}\] so when we look at the equation above and do this rule we would get \[\frac{d}{dx}x^4-5x^2 + 4= 4x^{4-1}-(2)5x^{2-1} = 4x^3-10x\]

Answer 6

oh okay

Answer 7

so now we have \[g \prime (x)= 4x^3 - 10x\] since we are looking for a minimum we need to set the whole equation to zero so \[4x^3 - 10x = 0\] now we need to solve for x

Answer 8

http://www.wolframalpha.com/input/?i=x%5E4-5x%5E2%2B4+ this website graphed your function and found the min and max and sorta shows you how i hope that i was at least some help

Answer 9

thanks!

Answer 10

no problem :)