Use the intermediate value theorem to determine whether or not f(x)=x^2+7x-7 and g(x)=4x+21 intersects on [-4,-1]. If applicable, find the point of intersection on the interval.
f(4) = 16 - 28 - 7 = -19
g(-4) = -16 + 21 = 5
g above f
f(-1) = 1 - 7 - 7 = -13
g(-1) = -4 + 21 = 17
g above f
They do not necessarily cross on the interval. However f might cross g twice in there being a parabola.
try solutions
x^2 + 7 x - 7 = 4 x + 21
x^2 + 3 x - 28 = 0
x = [ -3 +/- sqrt(9 + 112) ]/ 2
x = [ -3 +/- 11 ] / 2
x = 4 or -7
so nope