Prove the Form of a Function
$begingroup$
I asked a related question in oder to tackle this problem by myself, but still couldn't find a way to solve it despite a lot of efforts.
A function $f : R^2 to R$ satisfies $f(tx,ty) = t^2f(x, y)$ for all $t,x,y in R$. Assuming that
$f$ is continuously twice differentiable, show that:
$$
f(x,y) = ax^2 + bxy + cy^2
$$ for some
constants $a,b,c in R$.
calculus polynomials
asked Jan 15 at 17:23
A Slow LearnerA Slow Learner
466313
$endgroup$
add a comment |
$begingroup$
I asked a related question in oder to tackle this problem by myself, but still couldn't find a way to solve it despite a lot of efforts.
A function $f : R^2 to R$ satisfies $f(tx,ty) = t^2f(x, y)$ for all $t,x,y in R$. Assuming that
$f$ is continuously twice differentiable, show that:
$$
f(x,y) = ax^2 + bxy + cy^2
$$ for some
constants $a,b,c in R$.
calculus polynomials
asked Jan 15 at 17:23
A Slow LearnerA Slow Learner
466313
$endgroup$
$begingroup$
Can somebody help me?
$endgroup$
– A Slow Learner
Jan 16 at 2:36
add a comment |
$begingroup$
I asked a related question in oder to tackle this problem by myself, but still couldn't find a way to solve it despite a lot of efforts.
A function $f : R^2 to R$ satisfies $f(tx,ty) = t^2f(x, y)$ for all $t,x,y in R$. Assuming that
$f$ is continuously twice differentiable, show that:
$$
f(x,y) = ax^2 + bxy + cy^2
$$ for some
constants $a,b,c in R$.
calculus polynomials
asked Jan 15 at 17:23
A Slow LearnerA Slow Learner
466313
$endgroup$
I asked a related question in oder to tackle this problem by myself, but still couldn't find a way to solve it despite a lot of efforts.
A function $f : R^2 to R$ satisfies $f(tx,ty) = t^2f(x, y)$ for all $t,x,y in R$. Assuming that
$f$ is continuously twice differentiable, show that:
$$
f(x,y) = ax^2 + bxy + cy^2
$$ for some
constants $a,b,c in R$.
calculus polynomials
calculus polynomials
asked Jan 15 at 17:23
A Slow LearnerA Slow Learner
466313
asked Jan 15 at 17:23
A Slow LearnerA Slow Learner
466313
asked Jan 15 at 17:23
A Slow LearnerA Slow Learner
466313
asked Jan 15 at 17:23
A Slow LearnerA Slow Learner
466313
asked Jan 15 at 17:23
A Slow LearnerA Slow Learner
466313
466313
$begingroup$
Can somebody help me?
$endgroup$
– A Slow Learner
Jan 16 at 2:36
add a comment |
$begingroup$
Can somebody help me?
$endgroup$
– A Slow Learner
Jan 16 at 2:36
$begingroup$
Can somebody help me?
$endgroup$
– A Slow Learner
Jan 16 at 2:36
$begingroup$
Can somebody help me?
$endgroup$
– A Slow Learner
Jan 16 at 2:36
add a comment |
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– A Slow Learner
Jan 16 at 2:36