IB Mathematics Applications & Interpretation Topic SL…

Given $f(x) = x^3 - 5x^2 + 6x$

Find the derivative of $f(x)$ .

the coordinates of the turning points of $f(x)$ .

The volume of water in a storage tank is modeled by the function $V(t) = 2t^2 + 5t + 4$ , where represents the number of hours since filling began and is the volume of water in litres.

The growth of a plant species is modeled by the function $f(x) = 3x^2 + 2x + 5$ , where represents the number of weeks since planting and is the height of the plant in cm.

The total cost, in dollars, of producing $t$ items can be modeled by the function $h(t) = 3t^2 + 2t + 5$ , where is the number of items produced.

The concentration index $g(t)$ of a solution after $t$ minutes is modelled by $g(t)=\frac{5t-1}{2t+3}$ , where .

Find the derivative $V'(t)$ that represents the rate at which the volume of water changes over time.

Find the gradient of the volume curve at $t = 3$ .

the equation of the tangent line to the volume curve at the point where $t = 3$ hours. Give your answer in the form $y = mt + c$ .

the meaning of the gradient of the tangent line in the context of the volume of water in the tank.

Find the derivative $f'(x)$ that represents the rate of growth of the plant over time.

Find the gradient of the growth curve at $x = 4$ .

the equation of the tangent line to the growth curve at the point where $x = 4$ weeks. Give your answer in the form $y = mx + c$ .

the meaning of the gradient of the tangent line in the context of the plant's growth rate.

Find the derivative $h'(t)$ , which represents the rate of change of the cost as production increases.

the rate of change of the cost at $t = 4$ .

the equation of the tangent to the curve at the point where $t = 4$ .

the meaning of the gradient of the tangent line in this context. why this information is valuable for monitoring production costs.

the limit:

\lim_{t \to \infty} \frac{5t - 1}{2t + 3}

Find the derivative ( $g'(t)$ )

$g'(1)$ as a rate of change of $g$ at $t=1$ .

IB Mathematics Applications & Interpretation SL 5.1—introduction to Limits Questionbank

IB Mathematics Applications & Interpretation SL 5.1—introduction to Limits Questionbank

IB Mathematics Applications & Interpretation SL 5.1—introduction to Limits Questionbank

IB Mathematics Applications & Interpretation SL 5.1—introduction to Limits Questionbank

IB Mathematics Applications & Interpretation (AI) Topic SL 5.1—introduction to Limits Questionbank