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Further maths level 2 help!

Dear reader,
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!
Reply 1
Original post by Wolfram Alpha
Dear reader,
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!


f(x)=(1/2)x22x[br]f(x)=x2[br]f(x)=1f(x) = (1/2)x^2 - 2x[br]f'(x) = x - 2[br]f''(x) = 1

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).
Original post by ombtom
f(x)=(1/2)x22x[br]f(x)=x2[br]f(x)=1f(x) = (1/2)x^2 - 2x[br]f'(x) = x - 2[br]f''(x) = 1

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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