Cant draw this?

Question

Iv got this function 4x^4 -6x^2 +3

How to draw this function, to do that i need to calculate x1 x2 so how do u calculate those points so i draw it


Its not allowed to use a scientific calculator

Answer 1

Find first and second derivatives of the function, it will help.

Note that the second derivative is zero in the points of inflection of the function (i. e. turning points of the first derivative function).

Here blue is the function, red is its first derivative and green is its second derivative:
http://s210.photobucket.com/albums/bb64/oregfiu/?action=view¤t=derivatives.jpg
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Answer 2

Just find out values of y for equal steps of x (probably 1) and draw the points on your graph, then make a curve that goes through those points and it will end up a rough approximation of the curve you're looking for.

To find out what y is for each point of x, just do the calculation with x. For example, let's say you're drawing a point on the vertical line where x equals 2. 2^4 is 16, 4*16 is 64, 2^2 is 4, 6*4 is 24, so subtract 24 from 64 and add 3 at the end and you get 43, so you draw a point where x equals 2 and y equals 43. It's just a simple matter of replacing x with whatever x currently is and then doing the math.

Answer 3

The person above me pointed out some good points about max and min's, etc..

Generally, however, pick a variety of x-values:

try, for example, -10 to 10. Plug those integers in for 'x' and calculate 4x^4-6x^2+3 and see what you get for 'y'. Then on your x-y axis, plot the order pair.

For example, 4(2)^4-6(2)^2+3= 64 - 24 + 3 = -45

So plot (2, 43).

You will get an idea of what the graph is doing and focus in on a better range. Plot a bunch of points (x,y) and give it some flow when you graph it!

Answer 4

I'm assuming you want to graph this function in some valid domain and not just a random area. To do this, I would find out mins, maxes, and inflection points. You can find these by taking the derivative and solving for 0.

if f(x)=4x^4 - 6x^2 +3
then df(x)/dx = 16 x^3 -12 x -OR- x(16x^2-12)

x(16x^2-12)= 0

There are three solutions of which the easiest one is x = 0

16x^2-12 = 0
x^2 = 12/16 = 0.75
x = +/- (squareroot 0.75)

x = (-.866, 0, .866)

I would graph this from -1 to +1

x f(x)
-1 1
-.866 .75
-.6 1.36
-.2 2.77
0 3
.2 2.77
.6 1.36
.866 .75
1 1

Answer 5

Map some easy points:

x = 0 ==> (0, 3)
x = 1 ==> (1, 1)
x = 2 ==> (2, 43)
x = -1==> (-1, 1)
x = -2 ==> (-2, 43)

Do you know how to find the minimums and maximums of a function? If so, you can use this (derivatives) to determine where it turns from negative slopes to positive slopes and back again.

The first derivative of the function is:

16x³ - 12x

Set this to zero and solve for x:

16x³ - 12x = 0
4x(4x² - 3) = 0

At first glance, zero is one turning point. The other can be found using the quadratic formula:

4x² - 3 = 0

+/- sqrt(48)/8 = +/-sqrt(3)/2

If you'd like more help, please feel free to write.