5.4 Tangents and normals

5.4 Tangents and normals Quiz

IB Maths: Analysis and Approaches SL: Quiz

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5 questions, one answer each

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  1. 1. Find the gradient of the tangent to y=x3y=x^{3} at x=−1x=-1.

    • A. −3-3
    • B. 33
    • C. −1-1
    • D. 11

  2. 2. The tangent at a point has gradient −5-5. What is the gradient of the normal?

    • A. 55
    • B. −15-\frac{1}{5}
    • C. 15\frac{1}{5}
    • D. −5-5

  3. 3. Find the equation of the tangent to y=x2+1y=x^{2}+1 at (2, 5)(2,\,5).

    • A. y=4x−3y=4x-3
    • B. y=4x+5y=4x+5
    • C. y=2x+1y=2x+1
    • D. y=−14x+112y=-\frac{1}{4}x+\frac{11}{2}

  4. 4. At which point on y=x2−6xy=x^{2}-6x is the tangent horizontal?

    • A. (0, 0)(0,\,0)
    • B. (3, −9)(3,\,-9)
    • C. (6, 0)(6,\,0)
    • D. (−3, 27)(-3,\,27)

  5. 5. The normal to a curve at (1, 4)(1,\,4) has gradient 12\frac{1}{2}. What is the gradient of the curve at (1, 4)(1,\,4)?

    • A. 12\frac{1}{2}
    • B. 22
    • C. −2-2
    • D. −12-\frac{1}{2}

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