The approximate value of the function $f(x)=x^{3}-3 x+5$ at $x=1.99$ is

Question

Aicharya · Accepted Answer

$f(x)=x^{3}-3 x+5 \Rightarrow f^{\prime}(x)=3 x^{2}-3$ Let $a=2, h=-0.01$ $	herefore f(a)=f(2)=2^{3}-3(2)+5=7$ $f^{\prime}(a)=f^{\prime}(2)=3(2)^{2}-3=9$ We know that $f(a+h) = f(a)+h f^{\prime}(a)$ $f(1.99) = 7-(0.01)(9) = 7-0.09 = 6.91$

The approximate value of the function $f(x)=x^{3}-3 x+5$ at $x=1.99$ is

Solution