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Question 6

MildNo calculator
[Maximum mark: 5]

A function satisfies f′(x)=4x3−6xf'(x)=4x^3-6x and f(1)=2f(1)=2.

(a) Find f(x)f(x).[3]

(b) Find its vertical-axis intercept.[2]

Worked solution

Question 6 mark scheme

(a)

Integration gives f(x)=x4−3x2+Cf(x)=x^4-3x^2+C. Using f(1)=2f(1)=2 gives 1−3+C=21-3+C=2, so C=4C=4 and f(x)=x4−3x2+4f(x)=x^4-3x^2+4.

(b)

At x=0x=0, f(0)=4f(0)=4, so the intercept is (0,4)(0,4).

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