Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Measuring Change: Differentiation, Exercise 58: Chapter review

Let $f\left(x\right)=x-b\sqrt{x};x\ge 0,b\in R^{+}$. Find the intervals where $f$ is increasing and decreasing.

Let $f\left(x\right)=x-b\sqrt{x};x\ge 0,b\in R^{+}$. State the conditions on $b$ for $f$ to be concave up or concave down.

A rocket is launched vertically upwards. Its height, $h$ metres, $t$ seconds after it was launched, is given by $h\left(t\right)=49t-2.45t^2$. Find an expression for the velocity $v$ of the rocket at time $t$.

A rocket is launched vertically upwards. Its height, $h$ metres, $t$ seconds after it was launched, is given by $h\left(t\right)=49t-2.45t^2$. Find the maximum height of the rocket.

A particle travels in a straight line such that its velocity at any time $t$ is given by $v\left(t\right)=1+t-\sqrt{4t+9} \text{m}/\text{s}$. Find the particle's initial velocity.

A particle travels in a straight line such that its velocity at any time $t$ is given by $v\left(t\right)=1+t-\sqrt{4t+9} \text{m}/\text{s}$. Find the time when the particle is at rest.

A particle travels in a straight line such that its velocity at any time $t$ is given by $v\left(t\right)=1+t-\sqrt{4t+9} \text{m}/\text{s}$. Find the particle's acceleration at the instant it comes to rest.

A particle travels in a straight line such that its velocity at any time $t$ is given by $v\left(t\right)=1+t-\sqrt{4t+9} \text{m}/\text{s}$. Find the time interval(s) when the particle is slowing down and speeding up.