Derivative Problem: f’(1), f’(2), f’(3), and f’(5)

[SyaharaAden]

Homework Statement

Derivative Problem

Relevant Equations

Derivative

1. How to get f’(1), f’(2), f’(3), and f’(5)
2. How to calculate average speed change of y to changes in x in the interval [0,6]
3. Estimate value of f’+(0) and f’-(6)

pls help me about this graph, i dont know how to read this

 

[BvU]

Hello, and

Here at PF we need something from you before we are allowed to help (see guidelines). So:

What do you know about derivatives ? definition ?

$\$

 

[haruspex]

… and how is an average acceleration defined?

 

[Steve4Physics]

I don't think acceleration is needed. In fact, maybe the questions are not about motion at all. Possibly the intended questions are these:

1. Find $f’(1), f’(2), f’(3)$ and $f’(5)$ (where $f'$ denotes $\frac {dy}{dx}$).

2. Calculate the average rate of change of $y$ with respect to $x$ over the interval from $x=0$ to $x=6$.

3. Estimate the values of $f’_+(0)$ and $f_-'(6)$.

However, I suspect we might not hear from the poster again! (But - if they are reading this - I hope my suspicion is wrong!)

 

[haruspex]

I don't think acceleration is needed. In fact, maybe the questions are not about motion at all.

The OP's reference to speed change leads me to suppose the full question sets the context as motion.
Btw, I do not like the $f'(1)$ part. The diagram is not drawn correctly for that case. The straight line matches the slope of the curve somewhere around $x=\frac 12$, not at $x=1$.

 

[Steve4Physics]

The OP's reference to speed change leads me to suppose the full question sets the context as motion.

The phrase used by the OP is "calculate average speed change of y to changes in x ...".

There is no indication that ‘x’ represents time, so it seems possible (likely?) that the OP has used 'speed' thinking it is interchangeable with the term 'rate of change'. But we may never know!

Btw, I do not like the $f'(1)$ part. The diagram is not drawn correctly for that case. The straight line matches the slope of the curve somewhere around $x=\frac 12$, not at $x=1$.

Yes. I'd draw some of the other tangents slightly differently too.