- #1
madah12
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Homework Statement
Prove that for all y(x)=ax^2+bx+c where a is a constant !=0 and x is a real number that [tex]\frac{y'(x2)^2- y'(x1)^2}{(x2-x1)}[/tex] = 2y''(x)
Homework Equations
I don't know what to put here in mathematics but here...
y(x)=ax^2+bx+c
y'(x)=2ax+b
y''(x)=2a
The Attempt at a Solution
I made a lot of attempts and tried many thing but here is the one that looks like it works.
y''(x)=dy'(x)/dx
y''(x) * dy/dx = y'(x)dy'/dx
now here I don't know if its ok to take the dx es of the fraction
y''(x) dy= y'(x)dy'
integral from x1 to x2 (y''(x) dy)= integral from x1 to x2 (y'(x)dy')
and since y''(x)=2a so its a constant
y''(x)* (x2-x1)= 1/2 * (y'(x2)^2-y'(x1)^2)
2y''(x)= (y'(x2)^2-y'(x1)^2)/ (x2-x1)