Question

Use the intermediate value theorem to show that f(x) has a zero in the given interval. f(x)=2x^5-7x^3-4x^2+3; [0.6,0.7]

Answer 1

Since f(x) is continuous, IVT says that if one of the points on your interval is less than 0 and the other is greater than 0, then there is a some number 0.6<c<0.7 such that f(c) = 0.

So just plug each one of those into f(x) and if one is greater and the other is less than zero, you have shown there is a zero on that interval.

Answer 2

*is a number