03 - Instantaneous Rates of Change - Kuta Software

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Kuta Software - Infinite Calculus
Instantaneous Rates of Change
Name___________________________________
Date________________
Period____
For each problem, find the average rate of change of the function over the given interval and also find the
instantaneous rate of change at the leftmost value of the given interval.
8
1) y = 2x 2 − 2; [1, 3 2 ] x
2) y = − 1
x − 3 ; [0, 1 2 ]
y
8
y
6
6
4
4
2
2
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
x
For each problem, find the equation of the secant line that intersects the given points on the function and
also find the equation of the tangent line to the function at the leftmost given point. Sketch both lines for
comparison.
3) y = x 2 + x + 2; (−1, 2),
( − 1 2 , 7 4)
8
y
4) y =
1
x + 2 ( ; (−1, 1), − 1 2 , 2 3)
y
8
6
6
4
4
2
2
−8 −6 −4 −2 2 4 6 8
−2
x
−8 −6 −4 −2 2 4 6 8
−2
x
−4
−4
−6
−6
−8
−8

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Kuta Software - Infinite Calculus
Instantaneous Rates of Change
Name___________________________________
Date________________
Period____
For each problem, find the average rate of change of the function over the given interval and also find the
instantaneous rate of change at the leftmost value of the given interval.
8
1) y = 2x 2 − 2; [1, 3 2 ] x
2) y = − 1
x − 3 ; [0, 1 2 ]
y
8
y
6
6
4
4
2
2
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
−8 −6 −4 −2 2 4 6 8
−2
−4
−6
−8
x
Average: 5 Instant.: 4
Average: 2
15 Instant.: 1 9
For each problem, find the equation of the secant line that intersects the given points on the function and
also find the equation of the tangent line to the function at the leftmost given point. Sketch both lines for
comparison.
3) y = x 2 + x + 2; (−1, 2),
( − 1 2 , 7 4)
1
x + 2 ( ; (−1, 1), − 1 2 , 2 3)
4) y =
y
y
8
8
6
6
4
4
2
2
−8 −6 −4 −2 2 4 6 8 x
−8 −6 −4 −2 2 4 6 8 x
−2
−2
−4
−4
−6
−6
−8
−8
Secant: y = − 2 3 x + 1 3
Tangent: y = −x
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