Linear approximation?

Question

Suppose that we don't have the formula for g(x) but we know that g(3) = 3 and g'(x) is equal to the formula below for all x Sqrt(x^2+7) use linear approx. to find g(2.95) and g(3.05)

I have no idea how to start this..can someone clue me in please?

Answer 1

Assuming g'(x) = sqrt(x^2 + 7),

For x near 3,

g(x) ~ g(3) + g'(3)*(x-3)

g(2.95) ~ g(3) + g'(3)*(2.95 - 3) = 3 + sqrt(16)*(-0.05) = 2.8

Answer 2

Maybe this will help dunno but its worth a shot