Question

If $f(x) + x^2[f(x)]^3 = 10$ and $f(1) = 2$, find $f '(1)$

score 5.5k · Answer 1 · 2016-09-29 20:16:07

5.5k

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If $f(x) + x^2[f(x)]^3 = 10$ and $f(1) = 2$, find $f '(1)$

Published on 29 Sep 2016 - 20:16

score 341 · Answer 2 · 2016-09-30 18:06:25

341

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Functional recursion equations

Published on 30 Sep 2016 - 18:06

score 196 · Answer 3 · 2016-09-30 19:15:37

196

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Finding all functions $f(x)$ so that $f'(x)\sin x - f(x)\cos x = \sin^2x$

Published on 30 Sep 2016 - 19:15

score 23k · Answer 4 · 2016-10-02 01:59:09

23k

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How to find 4th degree polynomial equation from given points?

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score 78 · Answer 5 · 2016-10-04 12:18:17

78

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Let $f$ a periodic function which is differentiable on $\mathbb R$

Published on 04 Oct 2016 - 12:18

score 41 · Answer 6 · 2016-10-05 04:31:53

41

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Find a family of functions $f_{k,n}(z)$ with $f_{k,n}(z) = \frac{n}{k} \cdot z \cdot f^{'}_{k+1,n}(z) $

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score 326 · Answer 7 · 2016-10-05 11:37:14

326

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Find all functions $f:\mathbb Z \rightarrow \mathbb Z$ such that $f(0)=2$ and $f\left(x+f(x+2y)\right)=f(2x)+f(2y)$

Published on 05 Oct 2016 - 11:37

score 269 · Answer 8 · 2016-10-05 12:14:25

269

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Let $f$ a function which is differentiable on $[a,b]$ such that $f(a)=f(b)=f^\prime(a)=0$

Published on 05 Oct 2016 - 12:14

score 442 · Answer 9 · 2016-10-06 08:12:58

442

Views

Continuous functions satisfying $ f ( 1 - x ) = 1 - f \big( f ( x ) \big) $

Published on 06 Oct 2016 - 8:12

score 215 · Answer 10 · 2016-10-06 14:37:38

215

Views

Find all continuous functions $f(x+1)=f(x)+1$ and $f\left(\frac1x\right)=\frac1{x^2}f(x)$

Published on 06 Oct 2016 - 14:37

score 940 · Answer 11 · 2016-10-06 20:28:58

940

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Find $f(1986)$ if $f(1)=1$ and $f(x + y) = f(x) + f(y) - 2f(xy)$

Published on 06 Oct 2016 - 20:28

score 323 · Answer 12 · 2016-10-07 01:35:43

323

Views

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Published on 07 Oct 2016 - 1:35

score 268 · Answer 13 · 2016-10-07 17:34:38

268

Views

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score 153 · Answer 14 · 2016-10-08 12:43:49

153

Views

Prove that a function that satisfies $f(x^{2^{n}})=f(x)^{2^{n}}$ is constant given $f(0)=1$

Published on 08 Oct 2016 - 12:43

score 147 · Answer 15 · 2016-10-08 17:25:17

147

Views

Solution to functional equation $f(y,z)g(y+z)=h(y)$?

Published on 08 Oct 2016 - 17:25

List Question

If $f(x) + x^2[f(x)]^3 = 10$ and $f(1) = 2$, find $f '(1)$

Functional recursion equations

Finding all functions $f(x)$ so that $f'(x)\sin x - f(x)\cos x = \sin^2x$

How to find 4th degree polynomial equation from given points?

Let $f$ a periodic function which is differentiable on $\mathbb R$

Find a family of functions $f_{k,n}(z)$ with $f_{k,n}(z) = \frac{n}{k} \cdot z \cdot f^{'}_{k+1,n}(z) $

Find all functions $f:\mathbb Z \rightarrow \mathbb Z$ such that $f(0)=2$ and $f\left(x+f(x+2y)\right)=f(2x)+f(2y)$

Let $f$ a function which is differentiable on $[a,b]$ such that $f(a)=f(b)=f^\prime(a)=0$

Continuous functions satisfying $ f ( 1 - x ) = 1 - f \big( f ( x ) \big) $

Find all continuous functions $f(x+1)=f(x)+1$ and $f\left(\frac1x\right)=\frac1{x^2}f(x)$

Find $f(1986)$ if $f(1)=1$ and $f(x + y) = f(x) + f(y) - 2f(xy)$

Find all continuous functions from positive reals to positive reals such that $f(x)^2=f(x^2)$

Solving Cauchy's functional equation for Borel-measurable $f$

Prove that a function that satisfies $f(x^{2^{n}})=f(x)^{2^{n}}$ is constant given $f(0)=1$

Solution to functional equation $f(y,z)g(y+z)=h(y)$?

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