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TiliK225 [7]
1 year ago
7

Find the equation of the tangent line to g(x) = 4x² + 6x at x = 0 Simplify any fractions

Mathematics
2 answers:
jolli1 [7]1 year ago
8 0

Answer:

y = 6x

Step-by-step explanation:

Given:

\displaystyle \large{g(x)=4x^2+6x}

To find:

  • Tangent line equation at x = 0

First, derive the equation using power rules. Here are some power rules formula:

<u>Power Rules</u>

<u />\displaystyle \large{f(x) = x^n \to f'(x)=nx^{n-1}}\\\\\displaystyle \large{f(x)=kx^n \to f'(x)=knx^{n-1} \quad \tt{(k \ \ is \ \ constant.)}}\\\\\displaystyle \large{f(x)=k \to f'(x)=0 \quad \tt{(k \ \ is \ \ constant.)}

Apply power rules:

\displaystyle \large{g'(x)=4(2)x^{2-1}+6(1)x^{1-1}}\\\\\displaystyle \large{g'(x)=8x+6}

<u>Derivative Definition</u>

  • Derivative simply means slope or gradient at any points (x,y) and it is also rate of changes.

Since we want to find the slope at x = 0 (so that the line will be tangent to this point) then substitute x = 0 in g’(x):

\displaystyle \large{g'(0)=8(0)+6}\\\\\displaystyle \large{g'(0)=6}

Now we have slope = 6 at x = 0. Next, find y-value at x = 0, simply substitute x = 0 in g(x) to find y-value:

\displaystyle \large{g(0)=4(0)^2+6(0)}\\\\\displaystyle \large{g(0)=0}

So we have point (0,0) which is origin point. Before we head to next step, let’s review on what we have:

  • Slope at x = 0 is 6
  • Point (0,0)

Next, we use point-slope form to create the equation and convert to slope-intercept form:

<u>Point-Slope</u>

<u />\displaystyle \large{y-y_1=m(x-x_1)}

Determine:

  • \displaystyle \large{m=6}
  • \displaystyle \large{(x_1,y_1)=(0,0)}

Therefore:

\displaystyle \large{y-0=6(x-0)}\\\\\displaystyle \large{y=6x}

Therefore, the equation of tangent line to the parabola at x = 0 is y = 6x

Marina CMI [18]1 year ago
6 0

Answer:

y = 6x

To find equation,

1) Find Derivative

2) Find the slope at x

3) Find coordinates

<h3><u>Lets first Derive The Equation</u></h3>

\sf \rightarrow y = 4x^2 + 6x

\sf \rightarrow \dfrac{dy}{dx}  = (2)4x^{2-1} + (1)6x^{1-1}

\sf \rightarrow \dfrac{dy}{dx}  = 8x + 6

<u>Secondly find Slope at x = 0</u>

\sf \rightarrow \dfrac{dy}{dx}  = 8(0) + 6

\sf \rightarrow \dfrac{dy}{dx}  = 6      Yep so the slope(m) is 6.

                                       Recall, tangent line has the same slope.

<u>Now third step is to find coordinates</u>

At x = 0, y = 4x² + 6x ⇒ y = 4(0)² + 6(0) = 0   \star so coordinates: (0, 0)

Equation:

  • y - y₁ = m(x - x₁)
  • y - 0 = 6(x -0)
  • y = 6x
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3 years ago
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Kazeer [188]

a. First five terms: 9,13,17,21,25

b. Sum of first 25 terms = 1425

c. The given sequence is an arithmetic sequence because the common difference between two consecutive terms is same.

Further explanation:

Given

Formula of sequence

a_n=4n+5

<u>1. First 5 terms:</u>

For first 5 terms, we have to put n=1,2,...5,

So,

For\ n=1\\a_1=4(1)+5\\=4+5\\=9\\For\ n=2\\a_2=4(2)+5\\=8+5\\=13\\For n=3\\a_3=4(3)+5\\=12+5\\=17\\For\ n=4\\a_4= 4(4)+5\\=16+5\\=21\\For\ n=5\\a_5=4(5)+5\\=20+5\\=25\\First\ 5\ terms\ are: 9,13,17,21,25

<u>2. Sum of first 25 terms:</u>

For that we have to find 25th term first

a_{25} = 4(25)+5\\=100+5\\=105

The formula for sum is:

S_n=\frac{n}{2}(a_1+a_n)}\\Putting\ the\ values\\S_n=\frac{25}{2}(9+105)\\=12.5(114)\\=1425

<u>3. Type of sequence</u>

The given sequence is an arithmetic sequence because the common difference between two consecutive terms is same.

i.e.

d=4

Keywords: Arithmetic sequence, Sum of arithmetic sequence

Learn more about arithmetic sequence at:

  • brainly.com/question/3280369
  • brainly.com/question/7221312

#LearnwithBrainly

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Answer:

(n+2)^2+6

Step-by-step explanation:

Pattern 1 consists of

3+3\times 3+3 small squares (here n = 1 and 3\times 3=(1+2)\times (1+2)).

Pattern 2 consists of

3+4\times 4+3 small squares (here n = 2 and 4\times 4=(2+2)\times (2+2)).

Pattern 3 consists of

3+5\times 5+3 small squares (here n = 3 and 5\times 5=(3+2)\times (3+2)).

Thus, pattern n consists of

3+(n+2)\times (n+2)+3=6+(n+2)^2 small squares.

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I need answer in degrees! Thank you to anyone who answers ;P.
dedylja [7]

Answer:

x = 84

Step-by-step explanation:

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Sum of given angles = 132+54+90 = 132+144 = 276

So, x must cover the angle remaining from 276 to form 360, which is

360-276 = 84degrees.

Hope this helps

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jok3333 [9.3K]

Answer:

i think the answer is option 1           3

Step-by-step explanation:

i say this bc 3/4 times 4 is 3

hope this helps

if this is the correct answer plz mark brainliest.

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3 years ago
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