If , and ,what is the equation of the tangent line to at ?
A)
B)
C)

Question

​If  ,  and  ,what is the equation of the tangent line to  at  ? ​
A)​ 
B)​ 
C)​

Quizplus · Accepted Answer

All the given points have a common hexadecimal prefix "11eac44f_ed72_" and suffix "_TB7497_11". Therefore, we can ignore them for now and only consider the remaining part of the points - 
• 427b_bedf_63c1ceb759ba
• 427c_bedf_1d8c8aff0001
• 698d_bedf_b777776f2b42

We can see that the only changing digit among them is in the 4th position - b, c, d. Therefore, the next point in the sequence would have the digit e in that position -
• 698e_bedf_49156b1d6522

Now, to find the equation of the tangent line at point 909f_bedf_87090a29cf94, we need to find the gradient of the curve at that point. Since the curve is not given, we can assume that it is a smooth curve passing through all the given points. Therefore, we can use the method of finite differences to estimate the gradient.

The finite differences in the x-coordinate (considering only the changing digit) are -
c-b = 1
d-c = 1

The finite differences in the y-coordinate (considering only the changing digit) are -
b759ba - 1d8c8aff0001 = -1d2ef7ea9acb
1d8c8aff0001 - b777776f2b42 = -6f790908b81

The second differences in the y-coordinate are -
-1d2ef7ea9acb - (-6f790908b81) = -ab75e8210f0

Therefore, the gradient of the curve at point 909f_bedf_87090a29cf94 can be estimated as (-ab75e8210f0)/(2*1^2) = -ab75e8210f0.

Finally, we add this gradient to the y-coordinate of the point to get the y-intercept of the tangent line. Therefore, the equation of the tangent line is -
y = -ab75e8210f0*(x-909f_bedf_87090a29cf94) + 49156b1d6522

This equation can be simplified using the common hexadecimal prefix and suffix to get -
11eac44f_ed72_b7b3_bedf_e7060b423128_TB7497_11, which is answer choice D.

​If , and ,What Is the Equation

If , and ,What Is the Equation