p x = 20 x5 - 20 x4 + 24 x2 q x = 4 x2 p = 20 x4 - 20 x3 + 24 x, if xis not equal to 0 p / qx = ( 20 x4 - 20 x3 + 24 x) / (4 x2) = (5 x4 - 5 x3 + 6 x) / x2 So p / qx = 5 x2 - 5 x + 6/x if x is not equal to 0
x2 - 5x = 0x (x - 5) = 0x = 0andx = 5
x2 + 10x = 0 x2 + 10x + 25 = 25 (x + 5)2 = 25 x + 5 = +-5 x1 = 0 x2 =10
x2 - 10x + 25 = 0(x - 5)(x - 5) = 0x - 5 = 0x = 5
x2-5-4x2+3x = 0 -3x2+3x-5 = 0 or as 3x2-3x+5 = 0
x2 + 2y = 52 + 2*2 = 25 + 4 = 29
if x2 = 5 the value of x has to be 5 divided by 2 which is 2.5 x = 2.5
x1:y1 = x2:y2 4:-2 = x2:5 x2 = (4*5)/-2 x2 = -10
Centre = (0,0), radius = sqrt(5)
2.5
-2-5
f(x) = x2 + 3 ----> f(5) = (5)2 + 3 ----> f(5) = 28
The vertex has a minimum value of (-4, -11)
p x = 20 x5 - 20 x4 + 24 x2 q x = 4 x2 p = 20 x4 - 20 x3 + 24 x, if xis not equal to 0 p / qx = ( 20 x4 - 20 x3 + 24 x) / (4 x2) = (5 x4 - 5 x3 + 6 x) / x2 So p / qx = 5 x2 - 5 x + 6/x if x is not equal to 0
x2 - 5x = 0x (x - 5) = 0x = 0andx = 5
x = +5 or -5
Implicit: x2 + 2y = 5 Explicit : y = (5 - x2)/2