To graph the line we need two points; we already have one the point (4,2) now we need to find another one; to do this we get the equation of the line given by:

where m is the slope and (x1,y1) are a point throught the line. Plugging the values given we have:

Now we give a value to x and find the corresponding y. If x=0, then:

hence we have the point (0,-2).
Now that we have two points (0,-2) and (4,2) we graph them on the plane and join them with a straight line, hence the graph is:
Answer:
a = 4/27 - b/54
Step-by-step explanation:
27a+1/2b=4
Subtract 1/2 b from each side
27a+1/2b - 1/2 b=4-1/2 b
27a = 4 - 1/2 b
Divide each side by 27
27a/27 = 4/27 - 1/2 b/27
a = 4/27 - b/54
Answer:
You are rocking this... This is correct! :D
Step-by-step explanation:
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So, f[x] = 1/4x^2 - 1/2Ln(x)
<span>thus f'[x] = 1/4*2x - 1/2*(1/x) = x/2 - 1/2x </span>
<span>thus f'[x]^2 = (x^2)/4 - 2*(x/2)*(1/2x) + 1/(4x^2) = (x^2)/4 - 1/2 + 1/(4x^2) </span>
<span>thus f'[x]^2 + 1 = (x^2)/4 + 1/2 + 1/(4x^2) = (x/2 + 1/2x)^2 </span>
<span>thus Sqrt[...] = (x/2 + 1/2x) </span>
Critical points is where the derivative (slope) is zero or does not exist. So to do this we have to find the derivative of our function:

So we apply chain rule:
=

Set our first derivative to zero and solve for x:
3(x^2 - 1) * 2x = 0
So we can see that (by plugging in) 0, -1 and 1 makes our solution true
So our critical value is x = 0, x = -1, x = 1