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Excalidraw Data
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(7x-8)/(x^2-1)
quotient rule
(f’g - fg’)/g
f = 7x-8 g = x
f’ = 7 g’ = 2x
7(x^2-1) - 2x(7x-8) 7x^2 - 7 - 14x^2 + 16x (-7x^2 + 16x -7 )/(x^2-1)^2
5rt(2x+1)
chain rule
f’(g(x)) * g’(x)
f = x^(1/5) g = 2x+1
f’ = 1/5x^(-4/5) g’ = 2
1/5(2x+1)^(-4/5) * 2
2/5(2x+1)^(-4/5)
2/(5(2x+1)^4/5)
xy - x^2 = 10
product rule f = x g = y
f’ = 1 g’ = dy/dx
f’g + fg’ 1(y) + x(dy/dx)
y + x(dy/dx)
y + x(dy/dx) - 2x = 0 x(dy/dx) = 2x - y dy/dx = (2x-y)/x
2x^3 + 6x^2 - 90x + 3 6x^2 + 12x - 90
6x^2 + 12x - 90 = 0
6(x^2+2x-15) = 0 x^2 + 2x - 15 = 0 (x+5)(x-3)
-5 and 3 are critical numbers
-6 6(-6)^2 + 12(-6) - 90 54
-5
-4 6(-4)^2 + 12(-4) - 90 -42
3
5 6(5)^2 + 12(5) - 90 120
local maximum at -5, local minimum at 3
2x^3 + 6x^2 - 90x + 3
(-5,353) and (3,-159)
local maximum at (-5,353) local minimum at (3,-159)
2x
4x-8
4x-8 = 0 4x = 8 x = 2
0 2(0)^2 - 8(0) 0
2 2(2)^2 - 8(2) -8
7 2(7)^2 - 8(7) 42
absolute minimum at 2, -8 absolute maximum at 7, 42
Embedded Files
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