Question 90245
Let's evaluate {{{f(1)}}}


{{{f(x)=2x^5-7x+1}}} Start with the given polynomial



{{{f(1)=2(1)^5-7(1)+1}}} Plug in {{{x=1}}}



{{{f(1)=2(1)-7(1)+1}}} Raise 1 to the fifth power to get 1



{{{f(1)=2-7(1)+1}}} Multiply 2 by 1 to get 2



{{{f(1)=2-7+1}}} Multiply 7 by 1 to get 7



{{{f(1)=-4}}} Now combine like terms





Now let's evaluate {{{f(2)}}}




{{{f(x)=2x^5-7x+1}}} Start with the given polynomial



{{{f(2)=2(2)^5-7(2)+1}}} Plug in {{{x=2}}}



{{{f(2)=2(32)-7(2)+1}}} Raise 2 to the fifth power to get 32



{{{f(2)=64-7(2)+1}}} Multiply 2 by 32 to get 64



{{{f(2)=64-14+1}}} Multiply 7 by 2 to get 14



{{{f(2)=51}}} Now combine like terms


Since our y-value changes from a negative value to a positive value in the interval [1,2] this means there is a zero in this interval.