Question

Show that the function x^4+3z+1 have exactly one zero in the interval [-2,-1]

Answer 1

Answer:

The function f(x)=x^4+3x+1 is decreasing on the interval [-2,-1]. To show this, we take the derivative.

f'(x)=4x^3+3, which is less than zero whenever

4x^3<-3, which is the same asx^3<-3/4, or equivalently

x<(-3/4)^(1/3). Since (-3/4)^(1/3) is greater than -1, the derivative is negative on the whole interval, which means the function is decreasing and thus can have at most one zero there.

Now, f(-2)=(-2)^4+3(-2)+1=11, which is greater than 0, and f(-1)=(-1)^4+3(-1)+1=-1, less than

Answer 2

Answer:

answer will I think upper once is correct