How can there be a function with a second derivative greater than zero

In summary, the question is asking to prove or disprove if a function with a positive second derivative and a root at a is bounded below. A possible solution is to use the function f(x)=exp(-x)-x and show that it approaches positive infinity as x approaches negative infinity. However, it is unclear what happens as x approaches positive infinity.
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Aerosion
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Homework Statement



yet is approaching negative infiniti?

We were discussing a question that went "suppose f double prime (x)>0 and x ranges from negative infiniti to infiniti, and f(a)=0. Prove or disprove that f(x) is bounded below."

The man said that e^-x - x had a second derivative greater than zero, which i understand, but then how does it go to negative infiniti? I don't understand that, it should go to positive infiniti, right?

Homework Equations





The Attempt at a Solution

 
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  • #2
If f(x)=exp(-x)-x, f(x) does go to positive infinity as x->-infinity. What happens if x->+infinity?
 

FAQ: How can there be a function with a second derivative greater than zero

1. What is a second derivative and how is it calculated?

A second derivative is a mathematical concept that measures the rate of change of a function's slope. It is calculated by taking the derivative of the function's first derivative.

2. Can a function have a second derivative greater than zero?

Yes, a function can have a second derivative greater than zero. This means that the function's slope is increasing at an increasing rate.

3. How does a second derivative greater than zero affect the shape of a function's graph?

A second derivative greater than zero typically results in a concave up graph, meaning the graph curves upwards in a smile-like shape.

4. What does a second derivative greater than zero indicate about the behavior of a function?

A second derivative greater than zero indicates that the function is accelerating in the positive direction. This means that the function's rate of change is increasing.

5. Are there any real-world applications of a function with a second derivative greater than zero?

Yes, there are many real-world applications of a function with a second derivative greater than zero. For example, it can be used to model the acceleration of an object in motion, the growth rate of a population, or the increase in profits for a business.

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