# How do you find the maximum and minimum point in a graph?

- 0 votes

For example, when the question is "use the graph to find an estimate for the minimum value of Y" do you just look at the lowest value of Y on the graph or do you do something else?

## 5 Answers

- 0 votes

If you have the equation for the line, which you should do, you differentiate it, make it equal to zero, then solve to find the point.

For example if you have the graph y = x(2) + 7x + 5 (2) is squared

Differentiate:

dy/dx = 2x + 7

0 = 2x + 7

x = -3.5

You then insert this into the original equation to find y:

y = -3.5(2) + 7 * -3.5 + 5

y = -7.25

Minimum point is (-3.5, -7.25)

You know it is a minimum because it is a positive x(2), if it is a negative x(2) then it is a maximum point.

Hope I have been of assistance to you :)

- 0 votes

I thought you had to differentiate it twice? Differentiating once is to find gradients and differentiating twice is maximum and minimum points?

- 0 votes

Differentiating once works but can be harder to use at a higher level, at my level I find differentiating once much simpler, but you can differentiate twice and you get the second derivative and stuff however I believe you need to have an x value to work out the turning points? Not sure, my notes on it aren't very good so sorry I can't be of more help on that.

- 0 votes

The function of **differentiating twice** is to determine whether the point is **Local maximum** or **Local minimum.** This is not neccessary on a **Quadratic graph** because it either has a **Local maximum Or** a **Local minimum**, not both. Like "CoolKid" said, if the equation of the line is ** positive x^2 **( y= x^2 + 7x +5 ), then the line has a **Local minium**, the lowst point of the curve on the **y axis **where the gradient = 0. If the the equation of the line is **negative x^2** (y= -x^2 +7x +5), then the line has a **Local maximum**, the highest point of the curve on the **y axis** where the gradient = 0.

We use the second derivative when dealing with a **cubic equation**. This is because in a **cubic**, there is both a **Local maximum** and a **Local minimum.** After factorising the first derivative you will have two ** x** values. By substituting both these ** x** values into the second derivative we can determine if they are the **x co-ordinate** of a **Local maximum** or a **Local minimum.** If the value acheived is **positive**, the point on the graph will be a **Local minimum**. If the value acheived is **negative**, the point ont the graph will be a **Local maximum**.

Now you have determined which point will be a **Local maximum** and **Local minimum**, all you have to do is substitute the corresponding **x co-ordiante** into the original equation to find the ** y value**. With both the **Local maximum** and **Local minimum** you can now plot your **cubic graph**.