Question

The function f is twice differentiable with f(2)=1, f'(2)=4, and f''(2)=3. What is the value of the approximation of f(1.9) using the line tangent to the graph of f at x=2?

Answer 1

\[f(x+\Delta x)\approx f(x)+f'(x)(\Delta x)\]
\[f(1.9)\approx f(2)+f'(2)(1.9-2)\]
\[f(1.9)\approx 1+4(0.1)=1.4\]

Answer 2

Whoops. That should be 1-4(0.1)=0.6. :D

Answer 3

what is the triangle symbol? i havent learned that yet :(

Answer 4

That triangle symbol is called delta. It means some sort of change in a quantity.

Answer 5

thanks!

Answer 6

No problem. :D