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lord [1]
3 years ago
12

[Calculus, Derivatives] Can a function be differentiable at certain points even if the entire function is not differentiable?

Mathematics
1 answer:
koban [17]3 years ago
5 0

A function is differentiable if you can find the derivative at every point in its domain. In the case of f(x) = |x+2|, the function wouldn't be considered differentiable unless you specified a certain sub-interval such as (5,9) that doesn't include x = -2. Without clarifying the interval, the entire function overall is not differentiable even if there's only one point at issue here (because again we look at the entire domain). Though to be fair, you could easily say "the function f(x) = |x+2| is differentiable everywhere but x = -2" and would be correct. So it just depends on your wording really.

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Hi! I need help with the attached question in calc. Thank you:)
Elena L [17]

Answer:

3π square units.

Step-by-step explanation:

We can use the disk method.

Since we are revolving around AB, we have a vertical axis of revolution.

So, our representative rectangle will be horizontal.

R₁ is bounded by y = 9x.

So, x = y/9.

Our radius since our axis is AB will be 1 - x or 1 - y/9.

And we are integrating from y = 0 to y = 9.

By the disk method (for a vertical axis of revolution):

\displaystyle V=\pi \int_a^b [R(y)]^2\, dy

So:

\displaystyle V=\pi\int_0^9\Big(1-\frac{y}{9}\Big)^2\, dy

Simplify:

\displaystyle V=\pi\int_0^9(1-\frac{2y}{9}+\frac{y^2}{81})\, dy

Integrate:

\displaystyle V=\pi\Big[y-\frac{1}{9}y^2+\frac{1}{243}y^3\Big|_0^9\Big]

Evaluate (I ignored the 0):

\displaystyle V=\pi[9-\frac{1}{9}(9)^2+\frac{1}{243}(9^3)]=3\pi

The volume of the solid is 3π square units.

Note:

You can do this without calculus. Notice that R₁ revolved around AB is simply a right cone with radius 1 and height 9. Then by the volume for a cone formula:

\displaystyle V=\frac{1}{3}\pi(1)^2(9)=3\pi

We acquire the exact same answer.

8 0
2 years ago
Sophia bought 18 packs of lemonade each pack has 24 cans answer key
Juliette [100K]
Answer is 432 cans in total
18 packs times 24 cans in each is 432
5 0
2 years ago
Solve for x. 3x - 1 = 27 x = 10 x = 28/3 x = 26/3
frutty [35]

Answer:

x = 28/3

Step-by-step explanation:

3x - 1 = 27

Add 1 to each side

3x - 1+1 = 27+1

3x = 28

Divide by 3

3x/3 = 28/3

x = 28/3

6 0
2 years ago
What is the area of the following circle?
Marysya12 [62]

Answer:

Area = pi X r^2 = pi x (1)^2 = 3.14 x 1 = 3.14

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
SOMEONE HELP ME PLEASE
Novay_Z [31]
Y - 5 = -1/2(x-1)

hope this helps!
3 0
2 years ago
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