Can you please check my solution to the following problem? Clarify, where necess
ID: 3281878 • Letter: C
Question
Can you please check my solution to the following problem? Clarify, where necessary, and make more thorough, where possible If co +-+- Prove that co +c,x c2x2 - a for some x in (0.1) Solution: = a for some c01 c1, c2, a E R. Define f: [0,1] R Notice that f (x) co+c1x + c2x2 The function is a polynomial, so it is continuous on [0, 1] and differenti able on (0, 1) Thus, we can apply the mean value theorem tof. Note: C1(0)2 2 f(1) co +1 + 1-a by assumption By mean value theorem, there is an x E (0,1) such that = f(x) = f' (x) 1-0 . Co + c1x + c2x2 = a for some x in (0, 1)Explanation / Answer
function f(x) is a polynomial. Polynomials are continuous and differentiable for all real numbers. Hence f is continous in [0,1] and differentiable in (0,1)
the rest of the problem is perfect.
No corrections required.