SPM 2018 Add Maths Paper 1, Question 7Integration

Solved on video in English and Bahasa Melayu · 4 marks · Form 5, Integration · 4:22 video

The question

Diagram 2 shows the curve y = g(x). The straight line is a tangent to the curve. Given g'(x) = -4x + 8, find the equation of the curve.

[4 marks]

SPM 2018 Add Maths Paper 1, Question 7: the question as drawn in Eduly's video4:22

Step 1

The tangent line shown is horizontal at y = 11 and touches the curve only at its maximum point, so the maximum point of the curve has y-coordinate 11, and at that point g'(x) = 0.

Why this step

A flat tangent means zero gradient, and it touches the curve at the peak. So the peak has y = 11 and g'(x) = 0 there.

6 more steps, each with the reason for it, in the full solution

Final answer

g(x) = −2x² + 8x + 3

Where students lose marks

Watch out: don't forget + c after integrating. Use the peak (2, 11) to find c, not x = 0.

Watch every step of this question solved on video (4:22), with the reason behind each step and a box that checks your own answer.

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