Problem 42E

42. Suppose that we don’t have a formula for $g(x)$ but we know that $g(2)=-4$ and $g^{\prime}(x)=\sqrt{x^{2}+5}$ for all $x$.

(a) Use a linear approximation to estimate $g(1.95)$ and $g(2.05)$.

(b) Are your estimates in part (a) too large or too small? Explain.

Step-by-Step Solution