Question

let p(x) = x^5+8x^4-30x^3+30x^2-31x+22 what is the relationship between p(x) and f(x)= 5x^4+32x^3-90x^2+60x-31what do the values of p(1) and p(2) tell you about the values of f(x)

Answer 1

f(x) is derivative of p(x) with respect to x

Answer 2

ok I get that part I quess but what about the "what do the values of p(1) and p(2) tell you about the values of f(x)" part
Thanks btw

Answer 3

i assume there will be a sign change between those 2 values?

Answer 4

i think \(f(1)=0\) check it

Answer 5

sorry i meant \(p(1)=0\)

Answer 6

I got zero

Answer 7

yes as does \(p(2)=0\)

Answer 8

but I dont know what that means... i think I am a bit confused

Answer 9

it means there's a critical value between 1 and 2 where the tangent to the curve is horizontal

Answer 10

it means there's a zero of f(x) between x=1 and x=2