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# Further maths level 2 help!

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I require help with a question and you seem like the right person for this.
Find the turning point of the following functions:
1) y = 0.5x^2 - 2x
I first found dy/dx: x - 2 = 0 thus x = 2.
I substituted this into the original equation to find y: 0.5(4) -2(2) = 0 so my
coordinates are (2,0)
I found d2y/dx^2 to see if it is a maximum or minimum point: x = 0 which is a
positive value so I put down it is a minimum point. However, the correct
answer is that there are NO turning points for the above equation. Please
enlighten me ASAP. This is driving me nuts. Cheers!
2. (Original post by Wolfram Alpha)
I require help with a question and you seem like the right person for this.
Find the turning point of the following functions:
1) y = 0.5x^2 - 2x
I first found dy/dx: x - 2 = 0 thus x = 2.
I substituted this into the original equation to find y: 0.5(4) -2(2) = 0 so my
coordinates are (2,0)
I found d2y/dx^2 to see if it is a maximum or minimum point: x = 0 which is a
positive value so I put down it is a minimum point. However, the correct
answer is that there are NO turning points for the above equation. Please
enlighten me ASAP. This is driving me nuts. Cheers!

When f'(x) = 0, x = 2, so y = (1/2)(4) - 2(2) = -2, so the turning point is at (2, -2).

f''(2) = 1, since f''(x) is a constant, i.e. does not depend on x. As f''(x) > 0, this is a minimum point.

This can clearly be seen by plotting the graph (try desmos.com). Either you are looking at the wrong answer, the answer is wrong, or you have missed a range of values of x specified in the question (e.g. "Find the turning point of the following function, for 0<x<1", which would give no solutions).
3. (Original post by ombtom)

When f'(x) = 0, x = 2, so y = (1/2)(4) - 2(2) = -2, so the turning point is at (2, -2).

f''(2) = 1, since f''(x) is a constant, i.e. does not depend on x. As f''(x) > 0, this is a minimum point.

This can clearly be seen by plotting the graph (try desmos.com). Either you are looking at the wrong answer, the answer is wrong, or you have missed a range of values of x specified in the question (e.g. "Find the turning point of the following function, for 0<x<1", which would give no solutions).
Thanks very much.

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