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Point on a curve where the tangent is horizontal or vertical

This type of question, asked 5 times: 16 May 2023 S1, 23 Apr 2025 S1, 11 Apr 2026 S2, 14 May 2026 S1, 15 May 2026 S2. All 5 questions below, oldest first.

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  1. Question 1

    16 May 2023 S1

    146
    The abscissa of the point on the curve y=a ⁣(ex/a+e−x/a)y = a\!\left(e^{x/a} + e^{-x/a}\right) where the tangent is parallel to the X-axis is

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  2. Question 2

    23 Apr 2025 S1

    128
    The point on the curve 4y2−4y+2x−1=04y^{2}- 4y+ 2x- 1 = 0 at which the tangent becomes parallel toY-axis is

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  3. Question 3

    11 Apr 2026 S2

    75
    The tangent to the curve y2−xy+9=0y^2 - xy + 9 = 0 is vertical when

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  4. Question 4

    14 May 2026 S1

    76
    The point on the curve y=3x2−9x+8y = 3x^2 - 9x + 8 where the tangent is parallel to x-axis is

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  5. Question 5

    15 May 2026 S2

    77
    The coordinates of the point on the curve y=sin⁡(πx2)y = \sin\left(\dfrac{\pi x}{2}\right) at which the normal is parallel to the Y- axis are:

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