Skip to content

A student's working is shown below.

Consider the curve

y=199ex2−200200ex2

Let y=f(x). We have

f(−0.1)=0.0049502f(0.1)=0.0049502

Since both values are positive, the curve has no roots between −0.1 and 0.1.

  1. Give a simple counter-example to demonstrate that the student's reasoning is not generally true.

  2. By considering the value of f on some other interval, prove that f does, in fact, have a root within −0.1<x<0.1.


For (a), something like y=x2−4 would work, so long as you explain why this is a counter-example.


For (b), try f(0).


Give the root of f correct to 2 decimal places.