1. ## Maximum and Minimum

Find the largest and smallest values taken on by the function on the interval 0 < X < 2

I understand the procedure, finding the crit points first in which i got x = 1 for the real values.

Max = 1.66637 Correct to 4 significant figures.
Min = ?

2. ## Re: Maximum and Minimum

Hey fourhire.

Hint: What did you obtain for the first derivatives of this function?

3. ## Re: Maximum and Minimum

hey Chiro, f ' (x) = exp(x-1)^2 5cos(5x) + 2sin(5x)exp(x-1)^2(x-1)

4. ## Re: Maximum and Minimum

Now you have to find when that equals zero and then do a second derivative test to see where the minimum lies.

5. ## Re: Maximum and Minimum

Hi Chiro, so to clarify, f'(x)= 0 gives you maximum? and f''(x)=0 gives you minima?

6. ## Re: Maximum and Minimum

f'(x) = 0 helps you find the turning points which can be either a minimum, maximum, or point of inflexion.

Then for this particular x (or x's) that satisfy f'(x) = 0, the minimum satisfies f''(x) > 0, the maximum f''(x) < 0 and the point of inflexion satisfies f''(x) = 0 for the particular turning point for that particular x.