A slope field for the differential equation y ′ = 1 − y is shown in the accompanying figure. In each part, sketch the graph of the solution that satisfies the initial condition. a y 0 = − 1 b y 0 = 1 c y 0 = 2
A slope field for the differential equation y ′ = 1 − y is shown in the accompanying figure. In each part, sketch the graph of the solution that satisfies the initial condition. a y 0 = − 1 b y 0 = 1 c y 0 = 2
A slope field for the differential equation
y
′
=
1
−
y
is shown in the accompanying figure. In each part, sketch the graph of the solution that satisfies the initial condition.
a
y
0
=
−
1
b
y
0
=
1
c
y
0
=
2
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
For the following function f and real number a,
a. find the slope of the tangent line mtan
=
f' (a), and
b. find the equation of the tangent line to f at x = a.
f(x)=
2
=
a = 2
x2
a. Slope:
b. Equation of tangent line: y
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