Kuala Lumpur Trial 2025 Add Maths Paper 1, Question 14Differentiation

Solved on video in English · Form 5, Differentiation · 6:16 video

The question

(a)

Given the equation of a curve is y = 2x³ − 15x² + 24x + 6.

(a) Find the gradient function of the curve.

(b)

(b) Find the turning points of the curve.

(c)

Step 1

Differentiate term by term: d/dx(2x³) = 6x², d/dx(−15x²) = −30x, d/dx(24x) = 24, d/dx(6) = 0.

Why this step

Multiply by the power, then reduce the power by 1, so 2x³ gives 6x², not 6x³. The constant 6 never changes with x, so its gradient is 0.

1 more step, with the reason for it, in the full solution

Final answer

dy/dx = 6x² − 30x + 24

Where students lose marks

Watch out: lower the power by one (2x³ → 6x², not 6x³), and remember the constant 6 differentiates to 0.

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

Final answer

(1, 17) and (4, −10)

Where students lose marks

Watch out: substitute x = 1 and x = 4 into y, not dy/dx, or you'll just get 0 instead of the y-coordinate.

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

Final answer

(1, 17) maximum, (4, −10) minimum

Where students lose marks

Watch out: negative d²y/dx² means maximum and positive means minimum. Evaluate it at each x-value separately.

Watch every step of this question solved on video (6:16), with the reason behind each step and a box that checks your own answer.

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