Answer to Question #252389 in Calculus for howie

Question

Find the distinct interval of length 1 containing a root or solution of f(x)= x ³-3x+5 using IVT

Answer 1

$f(x)= x^3-3x+5 \\f(-2)=(-2)^3-3\times(-2)+5=-8+6+5=3>0 \\f(-3)=(-3)^3-3\times(-3)+5=-27+9+5=-13<0$

As $f(-2)>0 , f(-3)<0$

Then from IVT, there will be a root between $[-2,-3].$

This is only interval of length 1 for which , we will get the roots or solution of $f(x).$