1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lesechka [4]
3 years ago
6

6. Let f and g be differentiable functions

Mathematics
1 answer:
Julli [10]3 years ago
5 0

Answer:

(b) 1

Step-by-step explanation:

To differentiate h(x)=f(x)g(x) we will need the product rule:

h'(x)=f'(x)g(x)+f(x)g'(x).

We have h'(x)=f(x)g'(x), so the following equation is true by the transitive property:

f'(x)g(x)+f(x)g'(x)=f(x)g'(x)

By subtraction property we have:

f'(x)g(x)=0

Since g(x) \neq 0, then we can divide both sides by g(x):

f'(x)=\frac{0}{g(x)}

f'(x)=0

This implies f(x) is constant.

So we have that f(x)=c where c is a real number.

Since f(0)=1 and f(0)=c, then by transitive property 1=c.

So f(x)=1.

Checking:

h(x)=1 \cdot g(x)

h'(x)=g'(x)=1 \cdot g'(x)

So the following conditions were met.

You might be interested in
Х = 2y + 3<br> х = Зу — 4​
krek1111 [17]
I don’t even know :( sorry
8 0
2 years ago
Read 2 more answers
Evaluate the expression when C=1/2 and D=1/12<br> 3(1/4+C²)+2D<br> Please hurry!
Mkey [24]
Answer is 1 1/12
3(1/4 + 1/2^2)+ (2x1/12)
3/4+1/4+2/12 (you get to this part by distributing 3 throughout the parentheses)
9/12+3/12+2/12= 1 1/12 hope this helps
4 0
2 years ago
Read 2 more answers
A ball is thrown vertically upward.After t seconds its height(in feet)is given by the function h(t)=84t=16t^2.What is the maximu
Novay_Z [31]
21 seconds!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
3 0
2 years ago
PLEASE ANSWER ASAP! YOUR ANSWER MUST INCLUDE AN EXPLANATION IN ORDER TO RECEIVE 10 POINTS AND THE BRAINLIEST! THANKS!!!
7nadin3 [17]
The equation formula of the circle is (x-h)^2 + (y-k)^2 = r^2
where (h,k) the point of the  center of the circle
and (r) is the radius of the circle 
so if the center of the circle = (-2,-4)  
by subs. in the formula we get (x-(-2))^2 + (y-(-4))^2 = r^2 
then the equation will be (x+2)^2 + (y+4)^2 = r^2 
now we want to define the radius of the circle r
since point (3,8) lay on the circle so we can 
then subs. in the equation to get the radius 
(x+2)^2 +(y+4)^2 = r^2 
(3+2)^2 +(8+4)^2 = r^2 
25 + 144 = r^2 
r^2 = 169 
r= 13 
the radius of the circle is 13 
so by subs in the equation we get 
(x+2)^2 + (y+4)^2 = 169 
so it is the first answer in the choices 
8 0
3 years ago
What does 5/7c=13/14 equal
natita [175]
To find c, you must isolate it.
To do this, you must divide both sides by 5/7, since that is being multiplied by c and you must do the inverse to it to cancel it out in order to leave c by itself.

5/7c ÷ 5/7 = c

13/14 ÷ 5/7
To divide fractions, follow these steps:
Step 1- Turn the second fraction, 5/7 in this case, into its reciprocal. This means swapping the places of the numerator and denominator.
5/7 reciprocal = 7/5

Step 2- multiply the original first fraction and reciprocal second fraction.
13/14 • 7/5
13 • 7 = 91
14 • 5 = 70
13/14 ÷ 5/7 = 91/70

Step 3- Simplify if possible.
91/70
Since 70 can go into 90, you can turn this into a mixed number.
1 and 21/70
Now simplify 21/70.
Both can be divided by 7.
21 ÷ 7 = 3
70 ÷ 7 = 10
So simplified, 91/70 equals 1 and 3/10.
As a decimal, this is 1.3.

So the answer is c = 1.3, or 1 and 3/10.

Hope this helps :)
8 0
3 years ago
Other questions:
  • What two steps are necessary to put this equation into standard form x2-3x+16=6x-4
    11·2 answers
  • ε = {x: 2 ≤ x ≤30, x is an integer}, M = {even numbers}, P = {prime numbers}, T = {odd numbers} Find: M-T
    11·1 answer
  • The US Department of Energy reported that 48% of homes were heated by natural gas. A random sample of 333 homes in Oregon found
    10·1 answer
  • Write a program that will solve a quadratic equation: ax2 + bx + c = 0. The program must ask the user to enter the values for a,
    8·1 answer
  • How to find the area of congruent shapes
    5·2 answers
  • Help me for a cookie
    11·1 answer
  • Solve the inequality for v.<br> 89-11v ≤ 7v-55
    12·2 answers
  • Describe the overall shape of the histogram.
    11·2 answers
  • 3hr 60min 3s — 1hr 15min 55s
    9·1 answer
  • A cube has a volume of 343 3. What is the length of one of the edges of the cube?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!