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For the function y = x^(3) + 6x^(2) + 9x
Then
dy/dx = 3x^(2) + 12x + 9
At max/min dy/dx = 0
Hence
3x^(2) + 12x + 9 = 0
3(x^(2) + 4x + 3) = 0
Factor
(x + 1)(x + 3) = 0
Hence x = -1 & x = -3 are the turning point (max/min)
To determine if x = 0 at a max/min , the differentiate a second time
Hence
d2y/dx2 = 6x + 12 = 0 Are the max/min turning points.
Substitute , when x = -1
6(-1) + 12 = (+)6 minimum turning point .
x = -3
6(-3) + 12 = -6 maximum turning point.
When x = positive(+), then the curve is at a minimum.
When x = negative (-), then the curve is at a maximum turning point.
NB When d2y/dx2 = 0 is the 'point of inflexion' , where the curve goes from becoming steeper/shallower to shallower/steeper.
So when d2y/dx2 = 6x + 12 = 0
Then 6x = -12
x = -2 is the point of inflexion.
NNB When differentiating the differential answer gives the steeper of the gradient. So if you make the gradient zero ( dy/dx = 0) , there is no steepness, it is a flat horizontal line
What else can I help you with?
How do you find minimum area of a cricket ball using calculus?
i havent found yet will lwt u know later ..
Limits in calculus?
A limit in calculus is a value which a function, f(x), approaches at particular value of x. They can be used to find asymptotes, or boundaries, of a function or to find where a graph is going in ambiguous areas such as asymptotes, discontinuities, or at infinity. There are many different ways to find a limit, all depending on the particular function. If the function exists and is continuous at the value of x, then the corresponding y value, or f (x), is the limit at that value of x. However, if the function does not exist at that value of x, as happens in some trigonometric and rational functions, a number of calculus "tricks" can be applied: such as L'Hopital's Rule or cancelling out a common factor.
What is the vertex for the parabola y equals x squared plus 4x plus 5?
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Is calculus harder than physics?
Some people find calculus easier, others find physics easier. There is no general answer.
Is multivariable calculus hard?
That is not an easy question to answer. Many people find math hard in general and certainly some people find calculus hard to understand.Multivariable calculus is not really harder than single variable calculus. It is lots of fun since you learn about double and triple integrals, partial derivatives and lots more.I strongly suggest it for anyone who is thinking about taking it.
How would you find the range in a box and whiskers plot?
To find the range in a box and whiskers plot, you subtract the minimum value from the maximum value of the data set. The minimum and maximum values are represented by the endpoints of the whiskers. The formula is: Range = Maximum value - Minimum value. This gives you the overall spread of the data.
How can we find Range in case of frequency distribution?
Range = Maximum value - Minimum value
How do you find the range and domain of a graph function?
Assuming the standard x and y axes, the range is the maximum value of y minus minimum value of y; and the domain is the maximum value of x minus minimum value of x.
How do you find the Min value for y in this equation?
You didn't specify the equation. A minimum or maximum value of a function is often found by calculating the derivative of a function, writing an equation for derivative equal to zero, and then analyzing points where the derivative either doesn't exist, or is equal to zero. You'll find find information about this in introductory calculus books.
How do you determine wheather a quadratic function has a maximum or minimum and how do you find it?
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What are some examples of how to find the range in math?
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F(x) = | sin 3x | -3 find the maximum and minimum value?
if you have any doubts ask
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You cannot. The function f(x) = x2 + 1 has no real zeros. But it does have a minimum.
What is the range for the following set of measurements 3.1ml2.7ml4.6ml1.9ml8.7ml?
To find the range of the set of measurements, first identify the maximum and minimum values. The maximum value is 8.7 ml and the minimum value is 1.9 ml. The range is calculated by subtracting the minimum from the maximum: 8.7 ml - 1.9 ml = 6.8 ml. Therefore, the range of the set is 6.8 ml.
Where can you find the maximum or minimum value?
Just put the data in order and look at the biggest and smallest data entries.
How do you get minimum or maximum value of constant in a function?
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What is business calculus?
It's the college calculus class that students majoring in business must take. It includes the same concepts as any calculus class, but it discusses them in the business setting; like how to interpret definite integrals as useful business data, or how to find the maximum value on a curve that represents profit.
