Use the intermediate value
posted by Jenn .
Use the intermediate value theorem to show that the polynomial function has a zero in the given interval.
f(x)=9x^43x^2+5x1;[0,1]

There are a number of ways to do this, lets go to the idiot's guide to Math...
f(0)=1
f(1)=93+51=10
so how can one get to 10 from 1 by not crossing the y=0 axis? 
Not sure that is why I asked :)

The IVT is dependent on the fact that f(x) is continuous. That is, f(x) cannot get from 1 to 10 without being 0 somewhere on the way.
If f is not continuous, then there might be a hole at f=0, so there would be no guarantee that f(c)=0 for some 0<c<1. 
Reread the intermediate value theorem, it concludes that one can't get to 10 from 1 with a continuous function without passing the y=0 axis. Often, the mean value, and intermediate value theorem are written in math texts by lawyer wanttobe types, so complex, it loses its meaning.
Respond to this Question
Similar Questions

college algebra
Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval. f(x)=8x^54x^39x^29;[1,2] 
College Algebra
1. Use the Intermediate Value Theorem to show that the polynomial function has a zero in the given interval. f(x) = 13x^4  5x^2 +7x 1; [3,0] Enter the value of (3). 2. Use the Intermediate Value Theorem to show that the polynomial … 
college algebra, Please help!!
use the intermediate value theorem to show that the polynomial function has a zero in the given interval. f(x)=4x^3+3x^28x+7;[5,2] please show all work 
college algebraneed help please!!
use the intermediate value theorem to show that the polynomial function has a zero in the given interval. f(x)=x^5x^4+9x^35x^216x+5;[1.3,1.6] f(x)1.3= ? 
calculus
Use the intermediate value theorm to show that the polynomial function has a zero in the given interval f(x)=x^5x^4+8x^35x^214x5;[1.4;1.5] find the value of f(1.4) f(1.4)= find the value of f(1.5) f(1.5)= 
Use the intermediate value
Use the intermediate value theorem to show that the polynomial function has a zero in the given interval. f(x)=4x^3+6x^27x+1; [4,2] f(4)= 
Algebra
Use the intermediate theorem to show that the polynomial function value has a zero in the given interval f(x)=x^5x^4+8x^37x^217x+7; [1.6,1.8] Find the value of f(1.6) Find the value of f(1.8) 
intermediate value thorem
Use intermediate value theorem to show that the polynomial function has a zero in the given interval. f(3)= value of 0= 
algebra
Show Work Use the intermediate value theorem to show that the polynomial function has a zero in the given interval. f(x)=x^5x^4+4x^34x^220x+18 [1.5,1.8] 
algebra
Want to make sure I am doing this correctly. Use the Intermediate Value Theorem for polynomials to show that the polynomial function f(x)has zero between the numbers given. f(x)=3x^2x4 ; 1 and 2 3(1)^214=  2 below zero 3(2)^214= …