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Maths HL Intro to Calculus Questions

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On ‎10‎/‎16‎/‎2018 at 8:51 AM, hollabackguru said:

1. Prove that  1/(2x+1) = -2/(2x+1)^2 using first principles. 

2. Given the equation x^2 - 5, find the derivative of the function using first principles and then find the tangent. 

1. Use first principles formula. However, quotient rule is quicker alternative...

2. First you find the slope function of f(x) = x^2 - 5, which is parabola. To find the tanget, you need to know the point where they're asking you for the tangent, any point as (x,y) for example (1,2). As the slope of function f(x) x^2 - 5 is  f´(x) = 2x, just plug in the x-value of the point  (which is 1 in this case) --> 2 x 1 = 2. That's the SLOPE of the parabola at point (1,2). Hence, you can use the line equation: y - y0 = m (x - x0), where m = slope at the point, so 2. Substitute point (1,2) to function as x0 = 1 and y0 = 2 ------> y - 2 = 2(x-1)     and calculate it to get nice equation.

Q2.jpg

Q1.jpg

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