Apentix/AP Calculus AB/Unit 7: Differential Equations/Question

AP Calculus ABeasymcq1 pt

Consider the differential equation $\dfrac{dy}{dx} = x - 1$ . Which description of its slope field is correct?

A.Segments are horizontal along the vertical line

x = 1

and get steeper away from it.

B.Segments are horizontal along the horizontal line

y = 1

.

C.All segments in a given column have different slopes.

D.All segments in the field are horizontal.

Explanation

Core Concept

The slope is zero where $x = 1$ , and as $|x-1|$ grows the slope magnitude $|x-1|$ grows, so the field depends only on $x$ .

Correct Answer

ASegments are horizontal along the vertical line $x = 1$ and get steeper away from it.

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