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Recover a polynomial rule from derivative and tangent conditions

DIFFICULTYintrostandardchallengeexam
QUESTION TYPEMix of allChange
quadratic, derivative-plus-pointscubic, derivative-plus-pointsquadratic, tangent-line-plus-pointcubic, two-points-and-gradientNOWMix of allRecommended
Question 1 of 8

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Use the displayed curve information to recover the polynomial rule

\[q'(x)=-8x + 1\]
\[q(1)=1\]
(a)2 marks

Recover the rule for the polynomial and then evaluate it at the stated point. Enter the missing coefficients in the displayed rule

\[q(x)=\square\,x^{2} + \square\,x + 4\]
(b)1 mark

Calculate \(q(1)\) using the recovered rule