Chapter 2: Differentiation
Section 2.1: What Is a Derivative?
Example 2.1.1
The displacement of an object from a fixed origin O is described by the function st=18−20 t+9 t2−t3,t≥0, where the object is moving along a straight line. Determine the position and instantaneous velocity at time t=3, and the average velocity for the time-interval 2≤t≤4.
Solution
Control-drag st=…
Context Panel: Assign Function
st=18−20 t+9 t2−t3→assign as functions
Type st and press the Enter key.
Context Panel: Plots≻Plot Builder≻2-D plot Set 0≤t≤6 view axis[2]: 0,20
st→
Position at t=3
Write s3 Context Panel: Evaluate and Display Inline
s3 = 12
Instantaneous velocity as the limit of slopes of secant lines
Expression palette: Limit operator Apply to slopes of secant lines
limh→0s3+h−12h = 7
Average velocity as the slope of a secant line
Write the slope of the appropriate secant line Context Panel: Evaluate and Display Inline
s4−s24−2 = 6
The tutor can also be used to determine the slope of the tangent line. Alternatively, the Tangent command will return one of the following three items: the equation of the tangent line, the slope of the tangent line, a graph of the curve and the tangent line. Use this command to obtain the slope as follows.
Student:-Calculus1:-Tangentst,t=3,output=slope = 7
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