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
Vikki [24]
2 years ago
6

If f(x) = 2x^2 + 4x + 7, find f'(-5), using the definition of derivative. f'(-5) is the limit as x → -5

Mathematics
1 answer:
rosijanka [135]2 years ago
3 0

Using the limit definition of the derivative, you have

\displaystyle f'(-5) = \lim_{x\to-5} \frac{f(x) - f(-5)}{x - (-5)} = \lim_{x\to-5} \frac{(2x^2+4x+7) - 37}{x + 5}

Simplify the numerator:

(2<em>x</em> ² + 4<em>x</em> + 7) - 37 = 2<em>x</em> ² + 4<em>x</em> - 30

… = 2 (<em>x</em> ² + 2<em>x</em> - 15)

… = 2 (<em>x</em> + 5) (<em>x</em> - 3)

Then

\displaystyle f'(-5) = \lim_{x\to-5}\frac{2(x+5)(x-3)}{x+5} = \lim_{x\to-5} 2(x-3) = \boxed{-16}

• • •

For your second question in the comments, if <em>f(x)</em> = -2<em>x</em> ² + 3<em>x</em> - 7, then by the definition of the derivative, you have

\displaystyle f'(x) = \lim_{h\to0}\frac{f(x+h)-f(x)}h = \lim_{h\to0}\frac{(-2(x+h)^2+3(x+h)-7) - (-2x^2 + 3x - 7)}h

Simplify the numerator:

(-2 (<em>x</em> + <em>h</em>)² + 3 (<em>x</em> + <em>h</em>) - 7) - (-2<em>x</em> ² + 3<em>x</em> - 7)

… = (-2<em>x</em> ² - 4<em>xh</em> - 2<em>h</em> ² + 3<em>x</em> + 3<em>h</em> - 7) - (-2<em>x</em> ² + 3<em>x</em> - 7)

… = -4<em>xh</em> - 2<em>h</em> ² + 3<em>h</em>

Now compute the limit:

\displaystyle f'(x) = \lim_{h\to0}\frac{-4xh-2h^2+3h}h = \lim_{h\to0}(-4x-2h+3) = \boxed{-4x+3}

You might be interested in
If i have to put a relfection on triangle ABC across the y-axis.
deff fn [24]

Answer:

A coordinates are (-2,2)

B coordinates are (-2,4)

C coordinates are (-5,3)

6 0
3 years ago
A shipment of racquetballs with a mean diameter of 60 mm and a standard deviation of 0.9 mm is normally distributed. By how many
asambeis [7]
Mean 60 - 2(0.9) = 58.2
58.2 is 2 standard deviations from the mean.
8 0
3 years ago
Read 2 more answers
How to find the least common denominator
lesya [120]
Multiply the two numbers together
6 0
3 years ago
a) Suppose you are able to download 1 free song to your tablet daily and each additional download costs $0.59. If your monthly b
icang [17]
If 1 additional song costs $0.59, then there would be 26 additional songs downloaded. Because $15.34 divided by $0.59 is 26. 

Let x be the number of songs downloaded.

x = 28 + (15.34/0.59)
x = 28 + (26)
x = 54

You have 54 songs downloaded on your tablet. 

Hope this helps :)
7 0
3 years ago
How many countries in world
mariarad [96]

Answer:

There are 195 countries in the world today. This total comprises 193 countries that are member states of the United Nations and 2 countries that are non-member observer states: the Holy See and the State of Palestine

Not included in this total count of 195 countries are:

•Taiwan - the United Nations considers it represented by the People's Republic of China

•The Cook Islands and Niue, both states in free association with New Zealand which are members of several UN specialized agencies and have been recognized "full treaty-making capacity", but are neither member states nor non-member observer states.

•Dependencies (or dependent territories, dependent areas, dependencies) and Areas of Special Sovereignty (autonomous territories)  

•Other countries recognized by the United Nations as not being self-governing



8 0
3 years ago
Other questions:
  • Two interior angles of a triangle measure 34 degrees what is the measure of the third interior angle
    15·1 answer
  • A + b + c = 180 <br> b = 3a <br> c = 5a<br> Whats B
    14·2 answers
  • What are chicken nuggets never had them​
    9·2 answers
  • 3a+8+2ax≥3ax-4a what is a
    6·1 answer
  • There are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter.
    6·2 answers
  • 1. Which are true of x = log10 31,500? Select all that apply.
    13·1 answer
  • Round off 13,486 to the nearest hundred.
    6·2 answers
  • Can anyone help? Will give Brainly + 22 pts.
    14·1 answer
  • Help please I will give points
    8·2 answers
  • Jazmyn uses 2 gallons of paint to paint 5 walls. He uses 4 gallons of paint to paint 10 walls. How many gallons of paint does he
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!