Question

Use the intermediate value theorem to show that the function f(x)=x^2-7x+3 has a zero in the interval [0,1].

Answer 1

Intermediate Value Theorem basically says that if your starting point is below a point and your end point is above it, somewhere alone the road you have to pass the point! You can't hop from y=2 to y=3. Your line has to go through y=2.5

For you equation, you want to show that from x=0 to x=1, at some people y=0. Well, sub in 0 for x and see what you get. And then sub in 1 for x and see what you get.