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
anastassius [24]
3 years ago
13

If f(x) = 8x2 − x3, find f'(2) and use it to find an equation of the tangent line to the curve y = 8x2 − x3 at the point (2, 24)

.

Mathematics
2 answers:
slega [8]3 years ago
6 0
<span>f(x) = 8x2 − x3
f'(x) = 16x - 3x</span>²

f'(2) = 16(2) - 3(2)²
<span>f'(2) = 20

Using point-slope form:

y - y1 = m(x - x1)
y - 24 = 20 ( x - 2)

Therefore, the equation would be:

y = 20x - 16</span>
Svetlanka [38]3 years ago
6 0

f'(2) = 20

Equation of the tangent line → y = 20x - 16

<h3>Further explanation</h3>

To solve this problem there are several basic principles in Derivatives that need to be recalled, namely:

y = a ~ x^n \Rightarrow \frac{dy}{dx} = a ~ n ~ x^{n-1}

y = \sin x \Rightarrow \frac{dy}{dx} = \cos x

y = \cos x \Rightarrow \frac{dy}{dx} = - \sin x

y = u \times v \Rightarrow \frac{dy}{dx} = u' \times v + u \times v'

y = u \div v  \Rightarrow \frac{dy}{dx} = \frac{u' \times v - u \times v'}{v^2}

y = u^n \Rightarrow \frac{dy}{dx} = n \times u^{n-1} \times u'

\texttt{where u and v are functions in variable x}

\texttt{and u' and v' are derivatives of u and v}

Let us now tackle the problem !

<u>Given:</u>

f(x) = 8x^2 - x^3

f'(x) = 8(2x^{2-1}) - 3x^{3-1}

f'(x) = 16x^1 - 3x^2

f'(x) = 16x - 3x^2

f'(2) = 16(2) - 3(2)^2

f'(2) = 32 - 12

f'(2) = \boxed{20}

<em>Equation of the tangent line to the curve</em>

y - y_1 = m ( x - x_1 )

y - 24 = f'(2) ( x - 2 )

y - 24 = 20 ( x - 2 )

y - 24 = 20x - 40

y = 20x - 40 + 24

\boxed {y = 20x - 16}

<h3>Learn more</h3>
  • Implicit Differentiation : brainly.com/question/4711711
  • Logarithmic Differentiation : brainly.com/question/9226310
  • Calculus Problem : brainly.com/question/11237537

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Differentiation

Keywords: Maximum , Minimum , Value , Function , Variable , Derivation , Differentiation

You might be interested in
Find the slope of the tangent to y= -7Sin(x)+2cos(x) at x= 3π/4
BaLLatris [955]
Y = -7sin(x) + 2cos(x)
y = -7sin(3π/4) + 2cos(3π/4)
y = -7sin(9.42/4) + 2cos(9.42/4)
y = -7sin(2.355) + 2cos(2.355)
y = -7(0.03698381721) + 2(0.9993158646)
y = -0.2588867205 + 1.998631729
y = 1.739745009
6 0
3 years ago
En una reunión de 40 viejos piratas, 1/5 tenían una pata de palo y los 3/4 de ellos habían navegado en El Corsario. ¿Cuántos pir
Serga [27]

Answer:

spanish

Step-by-step explanation:

4 0
3 years ago
Which inequality describes this graph?
Alborosie

Answer:

x≠5

Step-by-step explanation:

An open circle means "less than" or "greater than", this means that anything is greater than or less than where the circle is placed. So, when an open circle is placed on a number line without any arrow, this means that that number is not equal to x.

5 0
3 years ago
Read 2 more answers
Write an equation in slope-intercept form for the line with y -intercept 2 and slope 3.
Ymorist [56]
Y=3X+2
Y=Mx+B therefore
8 0
3 years ago
Simplify. (-4x^4+x^2-4)+(5x^2-4)(−4x ​4 ​​ +x ​2 ​​ −4)+(5x ​2 ​​ −4)
zloy xaker [14]
-4x^4 - 15x^2 + 1 - 19/x^2 is your answer

Hope I helped :)
8 0
3 years ago
Other questions:
  • 1/10 of the m&amp;m in a bag are red and 1/5 are blue what fraction of the m&amp;m's are red and blue
    6·1 answer
  • The sum of a number and 19 is at least 8.3 what is the inequality and solution
    6·1 answer
  • √24 + √150 ?<br> What is equivalent?
    14·1 answer
  • If a seed is planted, it has a 90% chance of growing into a healthy plant. If 12 seeds are planted, what is the probability that
    12·1 answer
  • Evaluate sine, cosine, and tangent for -5pie/6
    14·1 answer
  • write the following integers in ascending order (smallest to biggest).1._5,2,1,_8 2. _4,_3,_5,2 3._10,_15,-7​
    7·1 answer
  • Please answer I’ll make brainliest
    14·1 answer
  • Which graph represents y=1/2(x+4)^2 +1
    15·1 answer
  • Gabby is 2 kg heavier than her sister who weighs 3.4 kg. what is their combined weight?​
    11·1 answer
  • Which numbers are 0.6 units away from 1.3 on a number line
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!