Question

Let f be a differentiable function such that f(3) = 2.345 and f' (x) = ln (x^2+ 1). What is the value of f (5)?

Answer 1

Use a linear approximation to $f(x)$ centered at $x=3$:

$f(x)\approx f(3) + f'(3)(x-3)$

Then

$f(5)\approx2.345+\ln(3^2+1)(5-3)\approx6.95$

which makes C the most likely choice.