if g(9)=20 and g(9)=2.41, estimate g(9.2). enter your answer rounded correctly to three decimal places.

Explanation:

Step1: Recall linear - approximation formula

The linear - approximation formula is $L(x)=g(a)+g^{\prime}(a)(x - a)$, where $a$ is the known point and $x$ is the point we want to estimate the function value at. Here, $a = 9$, $x=9.2$.

Step2: Substitute values into the formula

We know that $g(a)=g(9) = 20$, $g^{\prime}(a)=g^{\prime}(9)=2.41$, and $x - a=9.2 - 9=0.2$. Then $L(9.2)=g(9)+g^{\prime}(9)(9.2 - 9)$.

Step3: Calculate the estimate

$L(9.2)=20+2.41\times0.2=20 + 0.482$.

Answer:

$20.482$