Chapter 46 Polynomial Functions Let fx x4 gx x5 and hx x6

Chapter 4.6 Polynomial Functions

Let f(x) = x^4, g(x) = x^5 and h(x) = x^6 Find all numbers t in [0,1] such that F(t) =g(t)+h(t)

Solution

there is only one possible value that is t = 0 then only f(t) = g(t) + h( t) therefore 0=0

for all other values f(t) < g(t ) + h(t) for f(1) = 1 g(1) =1 and h(1) =1 therfore f(1 ) < g(1) + h( 1) i.e 1<2