1.9.17 Concavity and the second derivative (A-level only)

The concentration of a specific chemical dye in a test vat, $C$ (measured in mg/L), is modeled by the function

11\sqrt{t} + 10, \quad t > 0

where $t\,$ is the time in hours since the dye was introduced.

Determine the two values of $t\,$ for which the concentration is exactly 5 mg/L.

[4]

Find the value of $t\,$ for which $C′′(t)=1132\displaystyle C''(t) = \frac{11}{32}$ .

[4]

1.9.17 Concavity and the second derivative (A-level only) Questions

The concentration of a specific chemical dye in a test vat, $C$ (measured in mg/L), is modeled by the function

11\sqrt{t} + 10, \quad t > 0

where $t\,$ is the time in hours since the dye was introduced.

Determine the two values of $t\,$ for which the concentration is exactly 5 mg/L.

[4]

Find the value of $t\,$ for which $C′′(t)=1132\displaystyle C''(t) = \frac{11}{32}$ .

[4]