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Answer the following.
A Dolphin jumps and taken a path given by the equation , ( ), is the height of the Dolphin at any…
A Dolphin jumps and taken a path given by the equation $h(t) = \frac{1}{2}(-7t^2 + 3t + 2)$, ($t \ge 0$), $h(t)$ is the height of the Dolphin at any point of time. (Application)
(a)[1.5]
Is the function differentiable for $t \ge 0$? Justify.
(b)[1.5]
Find the instantaneous rate of change of height at $t = \frac{1}{14}$.
(c)[1.5]
$h(t)$ is increasing in $\left(-\infty, \frac{3}{14}\right)$. Is this true or false? Justify.
(d)[1.5]
Find the time at which the Dolphin will attains the maximum height. Also find the maximum height.
Answer
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From ISC 2026 Specimen Mathematics Paper 1, question 13(ii).