Given
[tex]f(x)=(x+1)^2\text{ }at\text{ }x=8[/tex]
Find
f(7.8)
Explanation
here , we use linear approximation to find the value of f(7.8)
so , we know
L(x) = f(a) + f'(a)(x-a)
f(a) = f(8) = (8+1)^2 = 81
now ,
[tex]\begin{gathered} f^{\prime}(x)=2(x+1) \\ f^{\prime}(a)=2(a+1) \\ f^{\prime}(8)=2(8+1)=18 \end{gathered}[/tex]
so , we have
[tex]\begin{gathered} L(x)=81+18(x-8) \\ L(7.8)=81+18(7.8-8) \\ L(7.8)=81+18(-0.2) \\ L(7.8)=81-3.6 \\ L(7.8)=77.4 \end{gathered}[/tex]
Final Answer
Hence , the correct option is A
