Which Is Greater: f(-2) or f(10)?

In summary, the question is asking for the comparison of the values of f(-2) and f(10) for the given derivative f'(x) = (1/4)x(x-6) and it is also mentioned that it is allowed to sketch f(x) using f'(x) graph but not take the integral directly. The conversation also discusses the symmetry of the graph and the data taken from the integral function. There is a request for suggestions or elaboration on the symmetry idea, but it is mentioned that taking the integral is not allowed.
  • #1
Sonata4004
3
0
Would you please help me with the question:

The graph of derivative f'(x)= (1/4)x(x-6) is given.
What value is greater f(-2) or f(10)?
It is permitted to sketch f(x) using f'(x) graph, but you can not take the integral of f'(x) directly.
 
Last edited:
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  • #2
Is that supposed to be f'(x)= (1/4)x(x-6)? The graph of that is a parabola which is symmetric about x= 3. The distance from -2 to 3 is 5 while the distance from 3 to 10 is 7.
 
  • #3
Thank you for reply,
The graph f(x) is not exactly symmetrical about x=3 since f(-2)=-3.67 while f(8)=-5.33, though the distance from 3 to -2 and 8 is the same.
The data is taken from integral function y=(1/12)x^3-(3/4)x^2.
 
  • #4
Does anybody have other suggestions? Or maybe some elaboration on the symmetry idea? It is right that f(10)>f(-2), but I don't know solid proof for this unless taking integral, which is out of range of permitted tools
 

Related to Which Is Greater: f(-2) or f(10)?

What is an increasing function?

An increasing function is a mathematical function where the output (y-value) increases as the input (x-value) increases. This means that as the value of x increases, the corresponding value of y also increases.

What is a decreasing function?

A decreasing function is a mathematical function where the output (y-value) decreases as the input (x-value) increases. This means that as the value of x increases, the corresponding value of y decreases.

How can you determine if a function is increasing or decreasing?

To determine if a function is increasing or decreasing, you can look at the slope or the derivative of the function. If the slope is positive, the function is increasing. If the slope is negative, the function is decreasing.

What is the difference between a strictly increasing function and a non-decreasing function?

A strictly increasing function is a function where the output only increases as the input increases. This means there are no repeated y-values. A non-decreasing function is a function where the output either increases or stays the same as the input increases. This means there may be repeated y-values.

What are some real-life examples of increasing or decreasing functions?

An example of an increasing function is the height of a growing plant over time. As time passes, the height of the plant increases. An example of a decreasing function is the temperature of a cup of coffee as it cools down. As time passes, the temperature decreases.

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