A slope field for an unknown differential equation is shown
MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties
Problem
A slope field for an unknown differential equation is shown. Near the point (3,2), the short segment appears to rise approximately 0.90 unit for every 0.60 unit it runs horizontally.
A differentiable function y=f(x) satisfies the differential equation and passes through (3,2).
(a) Estimate dxdy at (3,2) using the information from the slope segment.
(b) Write an equation for the line tangent to the graph of y=f(x) at (3,2) using your estimate from part (a).
(c) Use the tangent line found in part (b) to approximate the value of f(3.2). Show your reasoning.