Plotting a Continuous Function Graph with Given Data

[leprofece]

Plot a continue function graph with the following data o properties f(0)= 0 f of (-1) = 0 f of first derivative in 0 = 0?
f of first derivative in (1) = 0
first derivative (x) > 0 in x >1 and (0,1)
first derivative (x) < 0 in x < -1 and -1<x<0
see my graph is it correct?? where am I wrong

View attachment 2727

 

[Ackbach]

Plot a continue function graph with the following data o properties f(0)= 0 f of (-1) = 0 f of first derivative in 0 = 0?
f of first derivative in (1) = 0
first derivative (x) > 0 in x >1 and (0,1)
first derivative (x) < 0 in x < -1 and -1<x<0
see my graph is it correct?? where am I wrong

View attachment 2727

It's a bit difficult to decipher your requirements. Let me see if I have them correct here:

\begin{align*}
f(0)&=0 \quad \text{satisfied} \\
f(-1)&=0 \quad \text{not satisfied} \\
f'(0)&=0 \quad \text{satisfied} \\
f'(1)&=0 \quad \text{not satisfied} \\
f'(x)&>0 \; \forall \, x>1 \; \text{or} \; 0<x<1 \quad \text{satisfied} \\
f'(x)&<0 \; \forall \, x<-1 \; \text{or} \; -1<x<0 \quad \text{not satisfied}
\end{align*}

 

[leprofece]

we keep on bad
Why is not satisfied?? in this two points?' without a graph is for me very difficult to understand

 

[Ackbach]

If what I wrote is indeed your requirements, there is an inherent contradiction. You require a continuous function on $[-1,0]$, and the requirement $f'(x)<0$ whenever $-1<x<0$ implies that $f$ is differentiable on $(-1,0)$. But then Rolle's Theorem implies there must be a $c\in(-1,0)$ such that $f'(c)=0$, contradicting your last requirement that $f'(x)<0$ for all $-1<x<0$.

The requirements that I wrote down cannot all be satisfied. Could you please state the original problem, word-for-word?

Also, could you please write understandable English, as per http://mathhelpboards.com/rules/? I am not able to decipher your posts.

 

[leprofece]

Sketch a continuous graph with the following properties:

f(0)=0
f(-1)=0
f′(0)=0
f′(1)=0
f′(x)>0 for 0<x<1 and x>1
f′(x)<0 for (-1,0) and x<-1

About my english it is sorry to say I am from a latin Country and my mother tongue is not english

If what I wrote is indeed your requirements, there is an inherent contradiction. You require a continuous function on $[-1,0]$, and the requirement $f'(x)<0$ whenever $-1<x<0$ implies that $f$ is differentiable on $(-1,0)$. But then Rolle's Theorem implies there must be a $c\in(-1,0)$ such that $f'(c)=0$, contradicting your last requirement that $f'(x)<0$ for all $-1<x<0$.

The requirements that I wrote down cannot all be satisfied. Could you please state the original problem, word-for-word?

Also, could you please write understandable English, as per http://mathhelpboards.com/rules/? I am not able to decipher your posts.

 

[Ackbach]

Sketch a continuous graph with the following properties:

f(0)=0
f(-1)=0
f′(0)=0
f′(1)=0
f′(x)>0 for 0<x<1 and x>1
f′(x)<0 for (-1,0) and x<-1

About my english it is sorry to say I am from a latin Country and my mother tongue is not english

Thank you. Yes, the first two conditions contradict the last condition. It's not possible to create a graph with all these properties.

 

[leprofece]

no way thanks