# Need Help

#### Alan1990

##### New member
Dear Maths Help People,

I am hoping to go to Uni this autumn to study engineering after doing an ACCESS course, I feel like I am ok on most of the maths but in the uni mock test they have sent me before my real entry test I simply can't understand question 14. I have atatched it, if anyone could explain it to me that would be great.

Thanks,

Alan.

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#### Dr.Peterson

##### Elite Member
What have you learned about first and second derivatives?

#### Alan1990

##### New member
So far I've learned that the first derivative is the gradient of the original function at any point, and the second derivative is the rate of change of the first derivative at any point.

I'm not so hot on first principles but I've learned the formulas such as anx to the power of n-1 etc. Also how to get the derivative of sin and cosine waves and eulers number and natural logs.

#### Jomo

##### Elite Member
Point A and C both have the 1st derivative = 0.

Now start to the left of A and go to the right of A and see what the changes to the slope of the tangents lines are. Are they increasing (2nd der >0) or decreasing (2nd <0) or do they both increase and decrease around A?

Now do the same with point C.

What results do you get?

#### Otis

##### Senior Member
What does ev represent?

#### Alan1990

##### New member
Point A and C both have the 1st derivative = 0.

Now start to the left of A and go to the right of A and see what the changes to the slope of the tangents lines are. Are they increasing (2nd der >0) or decreasing (2nd <0) or do they both increase and decrease around A?

Now do the same with point C.

What results do you get?
I've been thinking about this and your clue I'm just not sure, I'm used to working with functions that already have a formula. It's like to the right of A the tangent would be positive, but to the left it would be negative, and with C to the left is would be negative and to the right positive. I don't really know what to do with that though. Is there a way to explain it in laymans terms?

#### Dr.Peterson

##### Elite Member
What does ev represent?

Do you mean "ve", as in "-ve"?

In some regions "-ve" is used to mean "negative". Of course, it's not good notation to write "x = negative", but at least we can know what is meant.

#### Dr.Peterson

##### Elite Member
I've been thinking about this and your clue I'm just not sure, I'm used to working with functions that already have a formula. It's like to the right of A the tangent would be positive, but to the left it would be negative, and with C to the left is would be negative and to the right positive. I don't really know what to do with that though. Is there a way to explain it in laymans terms?
This question is just about recognizing the sign of the first and second derivatives from a graph. You don't need a formula; just be aware that when a curve goes up to the right, the derivative is positive, and so on. And when the slope is changing as you move to the right, becoming smaller (that is, initially decreasing from a positive value, then reaching horizontal, then becoming steeper downward), the second derivative is negative. Just imagine following the curve with a ruler making a tangent line, and observe how the direction changes.

See this page for a lesson on this topic, with pictures: http://tutorial.math.lamar.edu/Classes/CalcI/ShapeofGraphPtII.aspx

#### Otis

##### Senior Member
Do you mean "ve" …
Yes, I mistyped what I had thought was a variable (or product of variables).

One more thing to remember here: =-ve means < 0, heh.

#### Jomo

##### Elite Member
I've been thinking about this and your clue I'm just not sure, I'm used to working with functions that already have a formula. It's like to the right of A the tangent would be positive, but to the left it would be negative, and with C to the left is would be negative and to the right positive. I don't really know what to do with that though. Is there a way to explain it in laymans terms?
Try again. What are the slopes of the tangents to the left of A? To the right of A. More importantly, we are not really looking to see if the slopes are positive or negative as we go from the left of A to the right of A. You need to understand that! Rather we are looking to see if the change is increasing or decreasing.

Here is an example. I owe $10,000 on my mortgage. Every month I bring down that bill. Is the change in what I owe increasing or decreasing? Does the fact that I always owe matter? I have a bank account with$10,000 in it. Every month I withdraw \$100. Is the change in my bank account increasing or decreasing? Does it matter that my balance is always positive?

#### Alan1990

##### New member
Thanks so much for all your answers guys, my maths test has been postponed due to the coronavirus so I am going to come back to this in a few weeks. Hopefully I will understand it a little more then, especially after reading all your answers. I have an assignment due in 2 days involving statistics which I have had no teaching on due to Corona so I am going to focus on that for now.