Question

Proof: There is a unique real number b such that f(x) = 2x^2 - 3x + 4 has a derivative of 0 at x=b.

Answer 1

Alright, proof by assume.
f'(x)=4x-3=0, 4x=3, x=3/4=b, which satisfies ∃b,(b∈ℝ)|f'(b)=0

Answer 2

In fact, ∃!b,(b∈ℝ)|f'(b)=0 is true because we can determine that there is only one solution such that 4x-3, since this is a first degree polynomial.

Answer 3

wow. that makes total sense. just have to look at it the right way. you like proofs, right? want to help more?

Answer 4

Sure.

Answer 5

Please post it as a separate question, though; don't like scrolling down.

Answer 6

posted.