Question

If you know that​ R' (20)=50 and​ R''(20)=-4, approximate​ R'(24)

Answer 1

Approximate R' by using a linear approximation: for x close enough to 24, you have

R'(x) ≈ L(x) = R' (20) + R'' (20) (x - 20)

Then

R' (24) ≈ R' (20) + R'' (20) (24 - 20) = -4 + 50 (24 - 20) = 196