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Polynomials and Rational Functions · Paper 2 — Free Maths AI HL Practice Questions

1MasterySAQ-SPolynomial functions and their graphs6 marksPaper 2~9 min
A company designs a water storage tank. The cross-section of the tank is modelled by the polynomial function f(x)=−0.02x3+0.3x2+0.6x+2f(x) = -0.02x^3 + 0.3x^2 + 0.6x + 2 for 0≤x≤120 \leq x \leq 12, where f(x)f(x) is the height of the tank wall (in metres) at a horizontal distance xx metres from the left edge.
(a)
State the degree of the polynomial and the value of the leading coefficient. [2 marks]
(b)
Calculate the height of the tank wall at the left edge (x=0x = 0) and at the right edge (x=12x = 12). [2 marks]
(c)
Determine the value of xx at which the maximum height occurs and state the maximum height, giving your answer correct to 3 significant figures. Hence comment on whether the maximum occurs at an endpoint or in the interior of the domain. [2 marks]
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Solutions

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