explain why the equation x^(5)-3x+1=0 must have a solution with 0 < x <1
Let f(x) = x^5 - 3x + 1
f(0) = 1
f(1) = -1
Since f is continuous on 0<=x<=1, it assumes all values between 1 and -1, which includes zero.
f(0) = 1
f(1) = -1
Since f is continuous on 0<=x<=1, it assumes all values between 1 and -1, which includes zero.