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
satela [25.4K]
3 years ago
10

Derivatives concept: Exercises using the definition of derivatives: (Full development)

Mathematics
1 answer:
krok68 [10]3 years ago
5 0

(A) <em>f(x)</em> = 7 is constant, so <em>f(x</em> + <em>h)</em> = 7, too, which makes <em>f(x</em> + <em>h)</em> - <em>f(x)</em> = 0. So <em>f'(x)</em> = 0.

(B) <em>f(x)</em> = 5<em>x</em> + 1   ==>   <em>f(x</em> + <em>h)</em> = 5 (<em>x</em> + <em>h</em>) + 1 = 5<em>x</em> + 5<em>h</em> + 1

==>   <em>f(x</em> + <em>h)</em> - <em>f(x)</em> = 5<em>h</em>

Then

\displaystyle f'(x) = \lim_{h\to0}\frac{5h}h = \lim_{h\to0}5 = 5

(C) <em>f(x)</em> = <em>x</em> ² + 3   ==>   <em>f(x</em> + <em>h)</em> = (<em>x</em> + <em>h</em>)² + 3 = <em>x</em> ² + 2<em>xh</em> + <em>h</em> ² + 3

==>   <em>f(x</em> + <em>h)</em> - <em>f(x)</em> = 2<em>xh</em> + <em>h</em> ²

\implies\displaystyle f'(x) = \lim_{h\to0}\frac{2xh+h^2}h = \lim_{h\to0}(2x+h) = 2x

(D) <em>f(x)</em> = <em>x</em> ² +<em> </em>4<em>x</em> - 1   ==>   <em>f(x</em> + <em>h)</em> = (<em>x</em> + <em>h</em>)² + 4 (<em>x</em> + <em>h</em>) - 1 = <em>x</em> ² + 2<em>xh</em> + <em>h</em> ² + 4<em>x</em> + 4<em>h</em> - 1

==>   <em>f(x</em> + <em>h)</em> - <em>f(x)</em> = 2<em>xh</em> + <em>h</em> ² + 4<em>h</em>

\implies \displaystyle f'(x) = \lim_{h\to0}\frac{2xh+h^2+4h}h = \lim_{h\to0}(2x+h+4) = 2x+4

You might be interested in
Find the area in square inches of the figure shown.
djverab [1.8K]

Answer:

8 * 17 = 136

39 * 36 = 1404

1482 + 136 = 1540

Step-by-step explanation:

5 0
3 years ago
Plz this is important number 2 plz
ololo11 [35]
Rounding it to the tens place so your answer for 12mm is going to be 10
7 0
3 years ago
What is the unit form of (2 tens 1 one) x 10
Masja [62]
WILLY, it is Two tens and one one multiplied by 10 is:

(20 + 1) * 10 = 21 * 10 = <span>210</span>
5 0
3 years ago
Graph the line with slope -1 passing through the point (-1,-4)
Lyrx [107]

Answer: look at pic

Step-by-step explanation:

y=mx+b

m:slope

b:y-intercept

m=-1 (slope) given in the question

y=-1x+b

Plug in the given point (-1,-4) then solve for b

-4=-1(-1)+b

b=-5

y=-x-5

then using the x-intercept and y-intercept you could graph the line

y-intercept = b = -5 (0,-5)

x-intercept (plug in y=0)

0=-x-5

x=-5 (-5,0)

4 0
3 years ago
Directions:Find the measures of the missing angles in each trapezoid. Will give brainliest for full answer.Posted for the 4th ti
Vladimir79 [104]

Step-by-step explanation:

m<M=m<L=110°

m<N=m<O=x → 2x+2(110°)=360° → x=70°

m<E=180°-22°=158°

m<A=360°-(88°+22°+158°)= 92°

m<D=m<O=61°

m<S=m<G=x → 2x+2(61°)=360° → x=238/2 = 119°

5 0
3 years ago
Read 2 more answers
Other questions:
  • How to solve this equation for y. need assistance please.<br> y-260=-11/5(x-100)
    14·1 answer
  • 10x3 tens in unit and standard form
    8·1 answer
  • What is the method of comparing Coefficient ​
    6·1 answer
  • What math problem can be made that equals 13 using all order of operations? (Parentheses exponents division addition subtraction
    8·1 answer
  • The variable z is directly proportional to x, and inversely proportional to y. When x is 11 and y is 14, z has the value 7.85714
    13·1 answer
  • Okay these last two are the last ones i need help on!
    7·1 answer
  • SOMEONE HELP PLSSS<br><br> 3. Which ratio would NOT be involved in the altitude or leg rule?
    14·1 answer
  • 15.00 + 1.75x &gt; 7.50 + 2.25
    15·1 answer
  • The lengths, in seconds, of four folk songs are
    12·1 answer
  • Hey there! BRAINLIEST! Lol, because I have no life whatsoever, but um if your on this question. Thank you. Please help me out! I
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!