$f(x)$ is differentiable or not on the interval?











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The question is to use the graph of $f$ to find is f differentiable or not on the given interval?



$f(x)=sqrt{4-x}$ following are the intervals $[0,4]$ and $[-5,0]$ and I have done this question as following



$f$ is differentiable:



enter image description here










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  • You missed a sign using ( or not using (?)) the chain rule, what did You think You proved and how is differentiability defined e.g. in the point $x=-4$ ( which is no interior point)....(Please use MathJax)
    – Peter Melech
    Nov 17 at 14:48












  • As the left hand limit is equal to right hand limit which proves that f exists so it can be stated that f is differentiable
    – Muhammad Usama
    Nov 17 at 14:50










  • $f$ exists, sure, but You didn't prove that, You proved that it is differentiable at $x=0$, though You missed a sign (Please use MathJax)
    – Peter Melech
    Nov 17 at 14:52















up vote
-2
down vote

favorite












The question is to use the graph of $f$ to find is f differentiable or not on the given interval?



$f(x)=sqrt{4-x}$ following are the intervals $[0,4]$ and $[-5,0]$ and I have done this question as following



$f$ is differentiable:



enter image description here










share|cite|improve this question
























  • You missed a sign using ( or not using (?)) the chain rule, what did You think You proved and how is differentiability defined e.g. in the point $x=-4$ ( which is no interior point)....(Please use MathJax)
    – Peter Melech
    Nov 17 at 14:48












  • As the left hand limit is equal to right hand limit which proves that f exists so it can be stated that f is differentiable
    – Muhammad Usama
    Nov 17 at 14:50










  • $f$ exists, sure, but You didn't prove that, You proved that it is differentiable at $x=0$, though You missed a sign (Please use MathJax)
    – Peter Melech
    Nov 17 at 14:52













up vote
-2
down vote

favorite









up vote
-2
down vote

favorite











The question is to use the graph of $f$ to find is f differentiable or not on the given interval?



$f(x)=sqrt{4-x}$ following are the intervals $[0,4]$ and $[-5,0]$ and I have done this question as following



$f$ is differentiable:



enter image description here










share|cite|improve this question















The question is to use the graph of $f$ to find is f differentiable or not on the given interval?



$f(x)=sqrt{4-x}$ following are the intervals $[0,4]$ and $[-5,0]$ and I have done this question as following



$f$ is differentiable:



enter image description here







functions derivatives






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Nov 17 at 14:37









mrtaurho

2,5941827




2,5941827










asked Nov 17 at 14:35









Muhammad Usama

11




11












  • You missed a sign using ( or not using (?)) the chain rule, what did You think You proved and how is differentiability defined e.g. in the point $x=-4$ ( which is no interior point)....(Please use MathJax)
    – Peter Melech
    Nov 17 at 14:48












  • As the left hand limit is equal to right hand limit which proves that f exists so it can be stated that f is differentiable
    – Muhammad Usama
    Nov 17 at 14:50










  • $f$ exists, sure, but You didn't prove that, You proved that it is differentiable at $x=0$, though You missed a sign (Please use MathJax)
    – Peter Melech
    Nov 17 at 14:52


















  • You missed a sign using ( or not using (?)) the chain rule, what did You think You proved and how is differentiability defined e.g. in the point $x=-4$ ( which is no interior point)....(Please use MathJax)
    – Peter Melech
    Nov 17 at 14:48












  • As the left hand limit is equal to right hand limit which proves that f exists so it can be stated that f is differentiable
    – Muhammad Usama
    Nov 17 at 14:50










  • $f$ exists, sure, but You didn't prove that, You proved that it is differentiable at $x=0$, though You missed a sign (Please use MathJax)
    – Peter Melech
    Nov 17 at 14:52
















You missed a sign using ( or not using (?)) the chain rule, what did You think You proved and how is differentiability defined e.g. in the point $x=-4$ ( which is no interior point)....(Please use MathJax)
– Peter Melech
Nov 17 at 14:48






You missed a sign using ( or not using (?)) the chain rule, what did You think You proved and how is differentiability defined e.g. in the point $x=-4$ ( which is no interior point)....(Please use MathJax)
– Peter Melech
Nov 17 at 14:48














As the left hand limit is equal to right hand limit which proves that f exists so it can be stated that f is differentiable
– Muhammad Usama
Nov 17 at 14:50




As the left hand limit is equal to right hand limit which proves that f exists so it can be stated that f is differentiable
– Muhammad Usama
Nov 17 at 14:50












$f$ exists, sure, but You didn't prove that, You proved that it is differentiable at $x=0$, though You missed a sign (Please use MathJax)
– Peter Melech
Nov 17 at 14:52




$f$ exists, sure, but You didn't prove that, You proved that it is differentiable at $x=0$, though You missed a sign (Please use MathJax)
– Peter Melech
Nov 17 at 14:52















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