Scaled

Mathematics Methods · Unit 3 · Topic 3.1

Further differentiation and applications

5 free questions, 3 calculator-free and 2 calculator-assumed, with worked solutions written like marking keys.

Calculator-assumedstandard

A population is modelled by P(t)=200e0.05tP(t) = 200e^{0.05t}, where tt is in years. Determine the rate of growth at t=10t = 10 years, correct to three decimal places.

Calculator-freestandard

For f(x)=x3−6x2+9xf(x) = x^3 - 6x^2 + 9x, determine f′′(1)f''(1).

Calculator-freefoundation

For f(x)=x3−6x2+9xf(x) = x^3 - 6x^2 + 9x, determine f′(2)f'(2).

Calculator-assumedstandard

A particle has position x(t)=t3−4t2+2tx(t) = t^3 - 4t^2 + 2t metres. Determine its acceleration at t=3t = 3 seconds.

Calculator-freefoundation

For f(x)=x3−3x2f(x) = x^3 - 3x^2, determine f′′(0)f''(0) and state whether the curve is concave up or concave down there.