Posted by lisa on .
Use the Euler Method with a step size of 0.2 to estimate f(3) where f′(x)=2x−7 and f(2)=4.
Your answer should be correct to two decimal places.

calculus 
Damon,
f(2.2) = f(2) + f'(2) (.2)
f(2.2) = 4 + (2*27) (.2)
f(2.2) = 4 + (47)(.2)
f(2.2) = 4 + (3)(.2)
f(2.2) = 3.4
now do f(2.4) the same way
then f(2.6) etc up to f(3) 
calculus 
Damon,
<img src="http://www.mathscoop.com/imagegallery/slopefields/2*x75555ffffff33006611120400ff0000240_23190.png " alt="Slope Field by MathScoop.com" />

calculus 
Damon,
from
http://www.mathscoop.com/calculus/differentialequations/eulermethodcalculator.php 
calculus 
Damon,
now exact
dy/dx = 2 x  7
integrate
y = x^2  7 x + c
when x = 2, y = 4
4 = 4 14 + c
c = 14
so
y = x^2  7 x + 14
so if x = 3
y = 9 21 + 14
y = 2 would be exact 
calculus 
Nate,
If that is the case, Damon, wouldn't the answer just be 1?