Calculus Problem Help

[us3rnotfound]

Some values of the function f are given in the following table.


x | 0.1 | 0.3 | 0.5 | 0.9 |
f(x)| 6.0 | 6.1 | 5.9 | 8.0 |

By using an average of estimates, one finds the best estimate of f'(0.3) to be

A. +0.20
B. -0.10
C. +0.05
D. -0.25

This is in a review for the final tomorrow. The answer is D, but could someone please explain how to get that answer?

Thanks

 

[StevenYoo]

man, i'm rusty...

 

[AgaBoogaBoo]

I would have guessed C but it's D so I'm not sure so here's a bump for you.

It's confusing because you don't know if the point of inflection is at .2 or .4 or even just .3

 

[hypn0tik]

Originally posted by: AgaBoogaBoo
I would have guessed C but it's D so I'm not sure so here's a bump for you.

It's confusing because you don't know if the point of inflection is at .2 or .4 or even just .3

The point of inflection doesn't matter.

Estimate the function to be straight line between the points .1, .3 and .5.

The slope of the function between .1 and .3 is +0.5
The slope of the function between .3 and .5 is -1.0

Average those slopes out to get -0.25

 

[us3rnotfound]

Oh wow, too ez :thumbsdown: 😀

 

[SaturnX]

or you can use the following:

f'(x) = ( f(x+h) - f(x-h) ) / 2h

The definition of the derivative..., where h is the difference between x-values in the sampled data.

Thus..

f'(0.3) = (5.9 - 6.0) / (2*0.2) = -0.25

--Mark