SOLUTION: Good day Determine the gradient of the tangents at the given points. f(x) = x� - x - 6 ....where y = -4 The answer is +-3 I just don't know how to get there

Question 980200: Good day
Determine the gradient of the tangents at the given points.
f(x) = x� - x - 6 ....where y = -4
The answer is +-3
I just don't know how to get there
Answer by Cromlix(4381) (Show Source): You can put this solution on YOUR website!
hi there,
First set up your equation:
f(x) = x^2 - x - 6
where y = -4
Therefore,
x^2 - x - 6 = -4
Collect like terms
x^2 - x - 6 + 4 = 0
x^2 - x - 2 = 0
Factorise
(x + 1)(x - 2)= 0
x + 1 = 0
x = -1
x - 2 = 0
x = +2
Differentiate:
y = x^2 - x - 6
dy/dx = 2x - 1
Substitute the two 'x' values
into the differentiated equation:
......
2x - 1
(x = - 1)
= 2(-1) - 1
= -2 - 1
= - 3
.......
2x - 1
(x = 2)
= 2(2) - 1
= 4 - 1
= 3
......
Therefore gradients are +-3
Hope this helps:-)
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