Tutor profile: Evan C.
What is the derivative of: 2x^2 + x + 1
Since all values are separated by + and -, you can apply the derivative to each part individually. Starting with 2x^2: First, you bring down the exponent and multiply it to the coefficient, then you subtract the exponent by 1. You get 2*2x^1 or 4x Next comes the x: Same thing as the last you get 1*1x^0. we know that anything raised to the 0 is 1, so 1*1*1 is 1. Finally you come to the 1: We know that the derivative of any constant is 0 So the solution is: 4x + 1
What is the Integral of: 3x^2 + x dx
First, apply the integral to both parts (since they are separated by a + or -) Starting with 3x^2: Add one to the exponent, and divide the coefficient by the new exponent: This becomes (3/3)x^3 or, simply, x^3 Next is the x: again, add one to the exponent and divide coefficient by new exponent: x is also 1x^1, so applying the step, you get (1/2)x^2 Since this is a general integral, and there is not a specified range, dont forget to put + C to account for a possible contant Finally, the answer is: x^3 + (1/2)x^2 + C
Find x: x^2 - x - 6 = 0
Using FOIL you need to find the multiples of 6 that add to -1 ( because it is -x) and multiply to -6 Multiples of 6 are: 1 and 6, 2 and 3 If you choose -3 and +2, they multiply to -6 and add to -1 You then add them to the FOIL equation, and you get (x-3)(x+2)=0 Solve for x: x= 3 and x= -2
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