2. Find the derivative of f (x) = 5x + 9 at x = 2. A) 9 B) 5 C) 0 D) 10<span><span> </span><span>f (x) = 5x + 9 </span><span>The first thing we should do in this case is to derive the function. </span><span>We have then: </span><span>f '(x) = 5 </span><span>We now evaluate the function for the value of x = 2. </span><span>We have then: </span><span> f '(2) = 5 </span><span>Answer: </span><span> the derivative of f (x) = 5x + 9 at x = 2 is: </span><span>B) 5
</span><span>3. Find the derivative of f (x) = 8 divided by x at x = -1.
</span><span>f (x) = 8 / x </span><span>The first thing we should do in this case is to derive the function. </span><span>We have then: </span><span>f '(x) = ((0 * x) - (1 * 8)) / (x ^ 2) </span><span> Rewriting we have: </span><span> f '(x) = -8 / (x ^ 2) </span><span>We now evaluate the function for the value of x = -1. </span><span> We have then: </span><span>f '(- 1) = -8 / ((- 1) ^ 2) </span><span>f '(- 1) = -8 </span><span>Answer: </span><span>The derivative of f (x) = 8 divided by x at x = -1 is: </span><span>-8
</span><span> 4. Find the derivative of f (x) = negative 11 divided by x at x = 9. </span><span> A) 11 divided by 9 </span><span>B) 81 divided by 11 </span><span>C) 9 divided by 11 </span><span> D) 11 divided by 81
</span><span> f (x) = -11 / x </span><span>The first thing we should do in this case is to derive the function. </span><span> We have then: </span><span>f '(x) = ((0 * x) - (1 * (- 11))) / (x ^ 2) </span><span>Rewriting we have: </span><span> f '(x) = 11 / (x ^ 2) </span><span>We now evaluate the function for the value of x = 9. </span><span>We have then: </span><span> f '(9) = 11 / ((9) ^ 2) </span><span> f '(9) = 11/81 </span><span>Answer: </span><span>the derivative of f (x) = negative 11 divided by x at x = 9 is: </span><span>D) 11 divided by 81
</span><span>5. The position of an object at time is given by s (t) = 3 - 4t. </span><span>Find the instantaneous velocity at t = 8 by finding the derivative. </span><span>s (t) = 3 - 4t </span><span>For this case, the first thing we must do is derive the given expression. </span><span>We have then: </span><span>s' (t) = - 4 </span><span>We evaluate now for t = 8 </span><span> s' (8) = - 4 </span><span>Answer: </span><span> the instantaneous velocity at t = 8 by finding the derivative is: </span><span>s' (8) = - 4</span></span>