1. Determine $f_{′}(2)$ for $f(x)=x_{2}+4x−1$. a. 7 c. 11 b. 8 d. 12
2. Determine the slope of the tangent to $y=1−5x+5x_{3}$ when $x=1$. a. -10 c. 10 b. 1 d. 15
3. An object moves in a straight line with its position at time $t$ seconds given by $s(t)=−3t+t_{2}$, where $s$ is measured in metres. Determine the velocity of the object when $t=3$. a. $−3m/s$ b. $0m/s$ c. $3m/s$ d. $6m/s$
5. For which value of $x$ is the derivative of $f(x)=(x−1)_{10}(x+2)_{5}$ equal to 0 ? a. -3 c. 1 b. 0 d. 2
4. The position function of an object moving horizontally along a straight line as a function of time is $s(t)=8t_{3}−4t_{2}$, in metres, at time, $t$, in seconds. Determine the acceleration of the object at $t=4s$. a. $184m/s_{2}$ c. $56m/s_{2}$ b. $248m/s_{2}$ d. $352m/s_{2}$
2. The position function of a moving object is $s(t)=t_{5}(3−t),t≥0$ in metres, at time $t$, in seconds. a. Calculate the object's velocity and acceleration at any time $t$. b. After how many seconds does the object stop? c. When does the motion of the object change direction? d. When does the object return to its original position?
3. Using Leibniz notation, apply the chain rule to determine $dxdy $ if $y=3(u_{2}+2u)_{2}$ and, $u=x−11 $ when $x=3$
4. The mass, $M$, in grams of a compound form during a chemical reaction can be modelled by the function $M(t)=t+2.26.3t $, where $t$ is the time in seconds after the start of the reaction. a) Determine the rate of change of the mass at $6s$ b) Is the rate of change of the mass ever negative? Explain.

Find for given function

use derivative rule