Find the stationary point on the line of y = 6x - x^2 and state whether this point is a maximum or a minimum
This question requires differentiating the equation to find where its gradient is equal to zero. Differentation is done via a simple equation --> if y = xn then dy/dx = nxn-1
Therefore if y = 6x - x2 , then dy/dx = 6(x0) - 2x1 , so dy/dx = 6 - 2x
The gradient is 0 at the stationary point, so 6 - 2x = 0 2x = 6 so x = 3
To find y, substitute (x=3) into the original formula to find y. y = 6(3) - 32 = 18 - 9 = 9
The stationary point is (3,9), and to find out whether this is a maximum or minimum, x=4 can be subbed in to the formula to find the next point on the line. y = 6(4) - 42 = 24 - 16 = 8 so the next point is (4,8)
This is below the stationary point, so we can see that (3,9) is a maximum.
PW
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