IB MATHEMATICS · AP CALCULUS · SAT MATH
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4. [Maximum mark: 10]
The function y is defined for x > 0 by
y = x² ln x.
(a) Find dy/dx. [4]
(b) Hence find the value of x when dy/dx = 2x. [6]
4. (a) dy/dx = 2x ln x + x
2x ln x + x = 2x
ln x = ½
x = √e
(Total 10 marks)
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The function f is defined by f(x) = x³ − 3x² + 2x + 1.
f′(x) = 3x² − 6x + 2
3x² − 6x + 2 = 0
x = 1 ± √3/3