# Max Extrema and Point of Inflection

• kari82
In summary, to find the extremas and points of inflections for g(t)= 1+(2+t)e^(-t), you need to find g(t)' and g(t)'' and then plug the values for t into the original function to get the corresponding y-coordinate. The critical point is (-1, 1+e) and the point of inflection is (0,3).
kari82
1. find the extremas and points of inflections

2. g(t)= 1+(2+t)e^(-t)

3. So i know you need to find g(t)' and g(t)''

g(t)'= -e^(-t)(1+t)
g(t)''= (t)e^(-t)

my critical point is t=-1 (max) and my point of inflection is t=o

How do I get to max extrema being (-1, 1+e) and point of inflection (0,3)? Thank you very much!

You've only given the x-coordinates of your critical point and point of inflection. The actual point is (t, g(t)). In other words you need to plug the values for t you have into the original function to get the corresponding y-coordinate.

Thank you so much! I knew it wasnt hard... I just couldn't figure it out. Thanks again!

## 1. What is a maxima or minima point?

A maxima or minima point, also known as an extremum, is a point on a graph where the function reaches its highest or lowest value. In other words, it is the peak or valley of a curve.

## 2. How do you find the maxima and minima points of a function?

To find the maxima and minima points of a function, you can take the derivative of the function and set it equal to zero. Then, solve for the x-values where the derivative is equal to zero. These x-values will be the coordinates of the maxima and minima points.

## 3. What is a point of inflection?

A point of inflection is a point on a graph where the concavity changes. In other words, it is the point where the curve changes from being concave up to concave down, or vice versa.

## 4. How do you determine the point of inflection of a function?

To find the point of inflection of a function, you can take the second derivative of the function and set it equal to zero. Then, solve for the x-value where the second derivative is equal to zero. This x-value will be the coordinate of the point of inflection.

## 5. Are all extremum points also points of inflection?

No, not all extremum points are points of inflection. A point of inflection is only present when the concavity of the function changes, whereas an extremum point can occur without a change in concavity. However, some extremum points can also be points of inflection if the concavity changes at the same point where the function reaches its maximum or minimum value.

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