Answer:
Step-by-step explanation:
The equation for a tangent line of f(x) in the point (a,f(a)) can be calculated as:
L(x) = f(a) + f'(a)(x-a)
Where L(x) is also call a linear approximation and f'(a) is the value of the derivative of f(x) in (a,f(a)).
So, the derivative of f(x) is:
Then, to find the linear approximation we are going to use the point (16, f(16)). So a is 16 and f(a) and f'(a) are calculated as:
Then, replacing the values, we get that the equation of the tangent line in (16,4) is:
Finally, the approximation for is: