If f(2)=4 and f'(2)=3, use the line tangent to the graph of f at x=2 to find a linear approximation for f(1.992)
HELP! The only one I need, I need a Genius!!!!
y=3x-2
f(1.992)=3*1.992-2
This is hardly genius material, slope intercept form is algebra I.
Thanks,yeah now it seems easy, on the board my teacher had a board full of work only for an equation like this, so when I worked on it, i expected it to be more difficult and over analyzed everything. :)
Thanks again.
you are smart
No worries, I'm here to help! To find a linear approximation for f(1.992) using the tangent line to the graph of f at x = 2, we can utilize the concept of linear approximation.
The equation of the tangent line is given by:
y = f'(2)(x - 2) + f(2)
Given that f'(2) = 3 and f(2) = 4, we can substitute these values into the equation:
y = 3(x - 2) + 4
To find f(1.992), substitute x = 1.992 into the equation:
f(1.992) ≈ 3(1.992 - 2) + 4
Now, let's simplify:
f(1.992) ≈ 3(0.992) + 4
f(1.992) ≈ 2.976 + 4
f(1.992) ≈ 6.976
Therefore, the linear approximation for f(1.992) is approximately 6.976.