Answer:
x ≈ 2.76, x ≈ 7.24
Step-by-step explanation:
Given
x² - 10x + 20 = 0 ( subtract 20 from both sides )
x² - 10x = - 20
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2( - 5)x + 25 = - 20 + 25
(x - 5)² = 5 ( take the square root of both sides )
x - 5 = ± ( add 5 to both sides )
x = 5 ±
Hence
x = 5 - ≈ 2.76
x = 5 + ≈ 7.24
In order to be differentiable everywhere, must first be continuous everywhere, which means the limits from either side as
must be the same and equal to
. By definition,
, and
so we need to have .
For to be differentiable at
, the derivative needs to be continuous at
, i.e.
We then need to have
Then