Find the derivative of the function y = 2x²(2x – 1) at the point x = -1?

A. 18

B. 16

C. -4

D. -6

QUICK ANSWER…

B

DETAILS…

The derivative of the function y = 2x²(2x – 1) at the point x = -1 is equal to 16.

If y = 2x²(2x – 1),

dy/dx can be determined using product rule.

Splitting the function into two,

Let u = 2x², and v = (2x – 1).

du/dx = 4x

dv/dx = 2

now product rule states thus:

dy/dx = vdu/dx + udv/dx

dy/dx = (2x – 1)(4x) + (2x²)(2)

dy/dx = 8x² – 4x + 4x²

dy/dx = 12x² – 4x

at point x = -1, we have:

dy/dx = 12(-1)² – 4(-1)

dy/dx = 12 + 4

dy/dx = 16

Now for the right answer to the above question:

1. Option A is incorrect.
2. Option B is correct.
3. C is not correct.
4. D is not the correct answer.

KEY-POINTS…

You may please note these/this:

• When two simple functions are combined as in the case of this question, use the product rule to differentiate.
• Product rule → dy/dx = vdu/dx + udv/dx.

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/ culled from 2021 JAMB-UTME MATHEMATICS question 8 /