# Tutor profile: Peter H.

## Questions

### Subject: Calculus

Using the chain rule, differentiate the following equation: f(x) = (6x^2 + 7x)^4

Substitute 6x^2 +7x for k The derivative of f(x) = the derivative of k^4 * the derivative of (6x^2+7x) Using power rules , f'(x) = 4k^3 * (12x + 7) Finally, Substitute 6x^2 +7x back for k: f'(x) = 4(6x^2 +7x )^3 * (12x + 7) Great work!

### Subject: C Programming

Do the following pieces of code output the same thing? Why or why not? Code 1: for (int i=0, i<9, i++){ printf("&d \n", i); } Code 2: int numbers[9]; for (int i=9, i>=0, i--){ number [i] = i; } for (int i=0, i<9, i++){ printf("&d \n", numbers[i]); }

Let's start with the first code as it appears simpler. Analyze what the for loop is doing: 1. We have an integer i starting at 0, we will go through the loop while i is less than 9, each time through the loop i will increase by 1. Thus we will go through the loop a total of 9 times. 2. In the loop we have one line of code. It prints the current i value, then makes a new line. 3. To summarize we will count from 0 to 8, inclusive, printing each number along the way followed by a new line. The output will look like this: 0 1 2 3 4 5 6 7 8 Time to tackle the second piece of code. Analyze what the first for loop is doing: 1. We have an integer i starting at 9, we will go through the loop while i is greater or equal to 0, each time through the loop i will decrease by 1. Thus we will go through the loop a total of 10 times. Hmmm... in the first piece of code we went through 9 times, let's make a note of this. 2. In the loop we have one line of code. It stores the current i value, in slot i of the integer array numbers[]. For example if i = 4 then numbers[4] = 4. 3. To summarize we will count down from 9 to 0, inclusive, storing each value of i, in the i slot of the array numbers[]. Analyze what the second for loop is doing: 1. We have an integer i starting at 0, we will go through the loop while i is less than 9, each time through the loop i will increase by 1. Thus we will go through the loop a total of 9 times. 2. In the loop we have one line of code. It prints numbers[i], BUT we know that numbers of i is equal to i itself. So this line just prints the current i value. 3. To summarize we will count from 0 to 8, inclusive, printing each number along the way followed by a new line. The output will look like this: 0 1 2 3 4 5 6 7 8 The outputs are the exact same! In the second piece of code we stored an extra number in slot numbers[9] = 9, but we never printed it, tricky!

### Subject: Algebra

Please find all possible values of x which satisfy the equation: x^2 + 3x + 2 = 0

Step 1: Factor the equation (x+1) (x+2) = 0 Step 2: Find the possible values of x that would make (x+1) (x+2) = 0 if x = -1 then (x+1) = (-1 + 1) = 0, 0 * (-1+2) = 0. Valid answer if if x = -2 then (x+2) = (-2 + 2) = 0, (-2 +1)*0 = 0. Valid answer Step 3: Summarize results. To satisfy the equation x^2 + 3x + 2 = 0, x = -1 or -2

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