Tutor profile: Prajna S.
How would you use calculus to find the maximum or minimum or inflection point of a graph?
You would find the first derivative of the function and equate it to zero. This would tell you at which x-coordinate, the graph's gradient equals zero. Once you have the x coordinate, you find the gradient just before and just after the point. If the order is +0-, it is a maximum. If the order is -0+, it is a minimum. If it is +0+ or -0-, it is an inflection point.
Explain the difference between current and charge.
Charge is the total number of charge dparticles that pass a particular point, where as current is the rate at which the charged particles flow. Current is defined as charge per unit time (I = Q/t). Think of charge as the total amount of water that falls off a waterfall, whereas current is the amount of water that falls every second. The total amount may be 1,000,000 kgs whereas the rate at which it falls would be 1,000,000 / (24 hrs * 60 min * 60 sec) = 11.57kg / seconds
List the process you would use to solve the following systems of equations, as well as your answer: A. 4x + 3y = 23 B. 3x + 2y = 16
You first want to eliminate a variable to reduce the systems of equations to one variable. 1) Pick a variable (let's pick x) and multiple the equations by a constant each such that their x-coefficients are equal. A*3 --> 12x + 9y = 69 B*4 --> 12x + 8y = 64 2) Subtract one equation from the other to elimiate the x-variable component of the equations. Using 3A - 4B, we get 12x + 9y - 12x - 8y = 69 - 64 Once we collect like terms, this reduces to y = 5 3) Simplify for the y-coefficient. If the y-coefficient of this resulting equation had not been 1, we would have had to further simplify it. 4) Substitute the y value back into either of the initial equations and rearrange for x. A. 4x + 3y = 23 -> 4x + 3(5) = 23 -> 4x + 15 = 23 -> 4x = 23 - 15 -> 4x = 8 -> x = 8/4 -> x = 2 So we have our solution (x, y) = (2, 5)
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