[麻省理工开放课程：微积分重点].Lecture.Notes.Big.Picture.Derivatives
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Δy We see later that this approaches cos x
Δx
MIT OpenCourseWare http://ocw.mit.edu
Resource: Highlights of Calculus
Gilbert Strang
The following may not correspond to a particular course on MIT OpenCourseWare, but has been provided by the author as an individual learning resource.
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
Practice Questions
1. For y = 2x3, what is the average slope = Δy from x = 1 to x = 2? Δx
2. What is the instant slope of y = 2x3 at x = 1?
3. y = xn has dy = nxn−1. What is dy when y(x) = 1 = x−1 ?
Then it goes downward for x > 1 dy
6A. What is the sign of for x < 1 and then for x > 1? dx
6B. What is the instant slope at x = 1? Δy
7. If y = sin x, write an expression for at any point x. Δx
dx
dx
x
4. For y = x−1, what is the average slope Δy from x = 1 to x = 1?
Δx
2
5.
What
is
the
instant
slope
of
y来自百度文库
=
x−1
at
x
=
1 ?
2
6. Suppose the graph of y(x) climbs up to its maximum at x = 1
Δx
MIT OpenCourseWare http://ocw.mit.edu
Resource: Highlights of Calculus
Gilbert Strang
The following may not correspond to a particular course on MIT OpenCourseWare, but has been provided by the author as an individual learning resource.
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
Practice Questions
1. For y = 2x3, what is the average slope = Δy from x = 1 to x = 2? Δx
2. What is the instant slope of y = 2x3 at x = 1?
3. y = xn has dy = nxn−1. What is dy when y(x) = 1 = x−1 ?
Then it goes downward for x > 1 dy
6A. What is the sign of for x < 1 and then for x > 1? dx
6B. What is the instant slope at x = 1? Δy
7. If y = sin x, write an expression for at any point x. Δx
dx
dx
x
4. For y = x−1, what is the average slope Δy from x = 1 to x = 1?
Δx
2
5.
What
is
the
instant
slope
of
y来自百度文库
=
x−1
at
x
=
1 ?
2
6. Suppose the graph of y(x) climbs up to its maximum at x = 1