Question

Use the intermediate value theorem to determine whether or not f(x)=x^2 + x + 2 and g(x)= -9x-7 intersect on [-7, -2]. If applicable, find the point of intersection on the interval.
Could I please see how to solve such a problem?

Answer 1

start with
\[x^2+x+2-(-9x-7)=x^2+10x+9\] then evaluate at at -7 and -2
if one value is positive and one is negative, then intermediate value theorem says it must be zero somewhere in between.
of course you can solve this using the quadratic formula as well

Answer 2

in fact you don't even need that. it factors as
\[(x+9)(x+1)\] so the zeros are at -1 and -9

Answer 3

which is not on the interval