For a given function f(x), the equation of tangent at a point x = a and y = f(a) is given by:
y - f(a) = f'(a).(x - a)
Hence, y = f(a) + f'(a).(x - a)
Also, since y = f(x), we can rewrite the above equation as:
f(x) = f(a) + f'(a).(x - a)
This is the linearization function for f(x), which is linear in nature with respect to x.
We have to find (46)1/2
So, the corresponding function will be f(x) =x1/2
We now need to choose "a". Let's choose "a" in close vicinity of 46 for which square root is easy to find.
Hence, let's choose a = 49
f(a) = f(49) = 491/2 = 7
f'(x) = 0.5x-1/2
f'(a) = 0.5 x 49-1/2 = 0.5 / 7 = 0.071428571 = 0.0714
Hence, f(x) = f(a) + f'(a).(x - a)
f(x) = x1/2 = 7 + 0.0714 (x - 49)
Now set x = 46.
461/2 = 7 + 0.0714 x (46 – 49) = 6.785714286 = 6.7857
Now set x = 50.
461/2 = 7 + 0.0714 x...
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