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
leonid [27]
3 years ago
11

Prove fermat's theorem for the case where f has a minimum at x0 (show f 0 (x0) = 0)

Mathematics
1 answer:
allochka39001 [22]3 years ago
6 0
Suppose that some value, c, is a point of a local minimum point.

The theorem states that if a function f is differentiable at a point c of local extremum, then f'(c) = 0.

This implies that the function f is continuous over the given interval. So there must be some value h such that f(c + h) - f(c) >= 0, where h is some infinitesimally small quantity.
As h approaches 0 from the negative side, then: \frac{f(c + h) - f(c)}{h} \leq 0 \text{, where h is approaching 0 from the negative side}
As h approaches 0 from the positive side, then: \frac{f(c + h) - f(c)}{h} \geq 0

Thus, f'(c) = 0
You might be interested in
What is the equation of this line?
ikadub [295]

Answer:

y=4/3x-1/3

Step-by-step explanation:

m=y2-y1/x2-x1

fill in the two points for the y's and the x's

then proceed to y = mx+b

Where:

m is the slope, and

b is the y-intercept

then you solve and <u>bam</u>!

8 0
3 years ago
Absolute value of 13
natima [27]

Answer:

13.

Step-by-step explanation: the absolute value is the distance away from 0 a number is. 13 is 13 numbers away from 0. the absolute value of negative 5 would simply be 5 since it is still 5 units away from zero, even though it is a negative number.

6 0
3 years ago
Andy wrote the equation of a line that has a slope of Step 2: y plus 2 equals StartFraction 3 Over 4 EndFraction x minus StartFr
nlexa [21]

answer is C

He made an error in Step 3. He should have subtracted 2 from both sides.

4 0
3 years ago
Read 2 more answers
5. (9) Letf- ((-2, 3), (-1, 1), (0, 0), (1,-1), (2,-3)) and let g- ((-3, 1), (-1, -2), (0, 2), (2, 2), (3, 1)j. Find: a. (g f (0
pashok25 [27]

Answer:  g(f(0)) = 2 and  (f ° g)(2) = -3.

Step-by-step explanation:  We are given the following two functions in the form of ordered pairs :

f = {(-2, 3), (-1, 1), (0, 0), (1,-1), (2,-3)}

g = {(-3, 1), (-1, -2), (0, 2), (2, 2), (3, 1)} .

We are to find g(f(0))  and   (f ° g)(2).

We know that, for any two functions p(x) and q(x), the composition of functions is defined as

(p\circ q)(x)=p(q(x)).

From the given information, we note that

f(0) = 0,  g(0) = 2,  g(2) = 2  and  f(2) = -3.

So, we get

g(f(0))=g(0)=2,\\\\(f\circ g)(2)=f(g(2))=f(2)=-3.

Thus,  g(f(0)) = 2 and  (f ° g)(2) = -3.

8 0
3 years ago
How is the numeral 55.12 written in words?
Ivan
Fifty-five and twelve hundreths
4 0
3 years ago
Read 2 more answers
Other questions:
  • I need to find the volume for number 10
    12·1 answer
  • Use the Remainder Theorem to determine which of the roots are roots of F(x). Show your work.
    15·1 answer
  • If someone gave you 100,000$ dollars, what would you spend it on, and why?
    11·2 answers
  • the cost of a 12-ounce bag of cashews is $5.86 what is the cost per ounce of the cashews to the nearest penny
    12·2 answers
  • Find the length of the arc round your answer to the nearest 10th
    6·1 answer
  • WILL MARK BRAINLIEST!
    7·2 answers
  • Can someone explain to me how to do this? I will give brainliest.
    14·1 answer
  • Can someone answer this ASAP thanks
    6·2 answers
  • Find the cost price where Profit=200, Profit%=10%
    6·2 answers
  • What should be added to (-10) to get (+10)​
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!