Given the function f(x)= -2x^3+x+6, find an interval of length one(for example (3,4) or (-1,0) or (-5,-4)) on the x-axis where there is guranteed to be a zero. Explain your answer.
Find some x-value where the value of y is negative. Find some other x-value where the value of y is positive. Pick x-values between these two, until you have x-values one unit apart, where one x-value gives a negative y-value and the other gives a positive y-value.
Zero has to be between negative and positive.