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3.5 Differentiation (A-level only)

3.5 Differentiation (A-level only)

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Question 11

A curve has the equation

y=ax2y = a^{x^2}y=ax2

where a a\,a is a constant greater than 1.

a.

Show that dydx=2xax2ln⁡a\dfrac{dy}{dx} = 2xa^{x^2}\ln adxdy​=2xax2lna.

[3]
b.

The tangent to the curve at the point (1,a)(1, a)(1,a) passes through the point (12,0)\displaystyle \left(\frac{1}{2}, 0\right)(21​,0). Find the value of aaa, giving your answer in exact form.

[3]
c.

By considering d2ydx2\dfrac{d^2y}{dx^2}dx2d2y​, show that the curve is convex for all values of xxx.

[2]
Markscheme

3.5 Differentiation (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.5 Differentiation (A-level only)

263 exam-style questions on CCEA A Level Maths 3.5 Differentiation (A-level only), covering 3.5.1 Differentiation (A-level only), 3.5.2 Differentiation (A-level only), 3.5.3 Differentiation (A-level only), 3.5.4 Differentiation (A-level only), 3.5.5 Differentiation (A-level only), and 3.5 Differentiation (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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