note that gradient = at x = a
calculate for each pair of functions and compare gradient
(a)
= 2x and
= - 1
at x = 4 : gradient = 8 and - 1 : 8 > - 1
(b)
= 2x + 3 and
= - 2
at x = 2 : gradient = 7 and - 2 and 7 > - 2
(c)
= 4x + 13 and
= 2
at x = - 7 : gradient = - 15 and 2 and 2 > - 15
(d)
= 6x - 5 and
= 2x - 2
at x = - 1 : gradient = - 11 and - 4 and - 4 > - 11
(e)
y = √x =
= 1/(2√x) and
= 2
at x = 9 : gradient = and 2 and 2 >
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Explanation:
I'll use the quadratic formula to find the roots or x intercepts. This slight detour allows us to factor without having to use guess-and-check methods.
The equation is of the form ax^2+bx+c = 0
This leads to...
Now use those roots to form these steps
Refer to the zero product property for more info.
Therefore, the original expression factors fully to (4x-5)(3x+1)
Use the FOIL rule to expand it out and you should get 12x^2-11x-5 again.
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We did that factoring so we could find the side lengths of the rectangle.
I'm using the fact that area = length*width
The order of length and width doesn't matter.
From here, we can then compute the perimeter of the rectangle
P = 2(L+W)
P = 2(4x-5+3x+1)
P = 2(7x-4)
P = 14x - 8
Distance formula ds = v(dx² + dy²) s = ? v(1 + (dy/dx)²) dx ......... s = the arc length y = 171 - x²/45
chegg
someone solved it on this
https://youtu.be/UGjXlMVdZvc
