The gradient of a function at any point (x,y) 2x – 6. If the function passes through (1,2), find the function.
- x\(^2\) - 6x - 5
- x\(^2\) - 6x + 5
- x\(^2\) - 6x - 3
-
x\(^2\) - 6x + 7
The correct answer is: D
Explanation
dy/dx = 2x - 6
y = ∫ 2x - 6
y = \(\frac{2x^2}{2} - 6 + c\)
y = x\(^2\) - 6x + c
passes through (1,2)
2 = 1\(^2\) - 6(1) + c
2 = 1 - 6 + c
c = 7
y = x\(^2\) - 6x + c
y = x\(^2\) - 6x + 7