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
nata0808 [166]
3 years ago
11

The line tangent to the graph of g(x) = x^{3}-4x+1 at the point (2, 1) is given by the formula

Mathematics
1 answer:
Usimov [2.4K]3 years ago
6 0

well, about A and D, I just plugged the values on the slope formula of

\bf \begin{array}{llll} g(x)=x^3-4x+1\\ L(x) = 8(x-2)+1 \end{array} \qquad \begin{cases} x_1=1.9\\ x_2=2.1 \end{cases}\implies \cfrac{f(b)-f(a)}{b-a}

for A the values are 8.01 and 8.0, so indeed those "slopes" are close. \textit{\huge \checkmark}

for D the values are -2.25 and 8.0, so no dice on that one.

for B, let's check the y-intercept for g(x), by setting x = 0, we end up g(0) = 0³-4(0)+1, which gives us g(0) = 1.

checking L(x) y-intercept, well, L(x) is in slope-intercept form, thus the +1 sticking out on the far right is the y-intercept, so, dice. \textit{\huge \checkmark}

for C, well, the slope if L(x) is 8, since it's in slope-intercept form, the derivative of g(x) is g'(x) = 3x² - 4, and thus g'(0) = -4, so no dice.

for E, do they intercept at (2,1)?  well, come on now, L(x) is a tangent line to g(x), so that's a must for a tangent. \textit{\huge \checkmark}

for F, we know the slope of the line L(x) is 8, is g'(2) = 8?  let's check

recall that g'(x) = 3x² - 4, so g'(2) = 3(2)² - 4, meaning g'(2) = 8, so, dice. \textit{\huge \checkmark}

You might be interested in
Problem 1: Joseph is going to buy a cell phone plan on his own. The most important thing for him is being able to text. So, he h
andriy [413]

Step-by-step explanation: lol like a dozen

4 0
3 years ago
Rewrite the expression using the
garik1379 [7]

Answer:

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
If a = 6 b=5, then find the value (a+b)​
ikadub [295]

Step-by-step explanation:

Put the numbers as the value is given

So,

(6+5)= 11 Answer

4 0
2 years ago
Read 2 more answers
When you divide a unit fraction by a whole number number, will the quotient be greater than or less than the unit fraction?
Salsk061 [2.6K]

Answer:

it will be less than

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
You are shopping for carpet for your living room which measures 19 feet by 12 feet. Charlie's Carpets sells carpet for $18 per s
Kamila [148]
----------------------------
Charlie's Carpets:
----------------------------
Carpet : $18/yd
Installation: $2/yd

Discount: 20% x $18 = 0.2 x 18 = $3.60
Carpet Price after discount = $18 - $3.60 = $14.40/yd²

Carpet Price with installation $14.40 + $2 = $16.40/yd²

----------------------------
Cindy's Carpet
----------------------------

Carpet = $18/yd²

Discount = 10% = 0.1 x $18 = $1.80
Price after Discount = $18 - $1.80 = $16.20/yd²

----------------------------
Summary:
----------------------------
Charlie's Carpet = $16.40/yd²
Cindy's Carpet = $16.20/yd²

CIndy's Carpet is cheaper.

----------------------------
Find Cost:
----------------------------
Length = 19 x 1/3 = 19/3 yards
Width = 12 x 1/3 = 4 yards

19/3 x 4 = 25 1/3 yd²

Cost = 25 1/3 x $16.20 = $410.40

------------------------------------------------------------------------------------
Answer: Cindy's Carpet is cheaper and it will cost $410.40.
------------------------------------------------------------------------------------

4 0
3 years ago
Other questions:
  • One of the factors of 6x^2-5x-4 is (2x-1). What is the other factor?
    15·1 answer
  • What is the square root of 81
    10·2 answers
  • 1. If f(x) = 3x² + x - 2, then f(-2) =<br> 8<br> 12<br> 32<br> -16
    13·2 answers
  • Help! Rational equations confuse me
    9·1 answer
  • What is 14 dividend by 12
    13·1 answer
  • How much of a $2,376.80 monthly net income is allotted for food if 23% is budgeted?
    8·1 answer
  • Which mixed number is equivalent to 606/100
    11·1 answer
  • 8.17 8.073 8.2<br> 8.03 8.063<br> 8.016<br> Least to greatest
    8·2 answers
  • HELP ME ASAP PLEASEEEEEEEE
    13·2 answers
  • 25:50=4x:8. What is the value of X​
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!