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skelet666 [1.2K]
2 years ago
11

Estimate graphically the local maximum and local minimum of f(x) = 4x2 + 3x + 2

Mathematics
2 answers:
Juliette [100K]2 years ago
6 0
Hope this helps you. If you need any help regarding how to sketch graph, ping me

jarptica [38.1K]2 years ago
4 0
Seeing the graph from desmos.com, we know there is only one place where the graph will go up then down, or down then up given that the maximum exponent of x is it squared. That place, as seen, is -0.375 for the minimum as it goes down then up. There's no maximum in sight :(

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Solve the in quality x plus 1<7
RUDIKE [14]

Answer:

x<6

Step-by-step explanation:

x+1 < 7

Subtract 1 from each side

x+1-1<7-1

x <6

7 0
3 years ago
Pls help these are due TODAY!!!!
Tamiku [17]

Answer:

10

Step-by-step explanation:

the two triangles formed from c are similar which means the sides are proportional

the proportion of one length of a side of a triangle to a similar side of the other triangle is the same as another side to its corresponding side of the other triangle. god im bad explaining stuff

anyway 2 is to 8 what 2.5 is to length BC. 2/8 = 2.5/x

    -crossmultiplyyy

2*x = 2.5*8

2x = 20

2x/2 = 20/2

x = 10

5 0
3 years ago
Find the derivative of following function.
Aleks04 [339]

Answer:

\displaystyle y' = \frac{\big( -2 \cos x \sin x - \frac{3}{2\sqrt{x}} \big) \big( \tan^2 x + 5x \big) + \big( \cos^2 x - 3\sqrt{x} + 6 \big) \big( 2 \sec^2 x \tan x + 5 \big)}{ \big( \csc^2 x + 3 \big) \big( \sin^2 x + 6 \big)} + \frac{2 \cot x \csc^2 x \big( \cos^2 x - 3\sqrt{x} + 6 \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big)^2 \big( \sin^2x + 6 \big)} - \frac{2 \cos x \sin x \big( \cos^2 x - 3\sqrt{x}  + 6 \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big) \big( \sin^2 x + 6 \big)^2}

General Formulas and Concepts:
<u>Calculus</u>

Differentiation

  • Derivatives
  • Derivative Notation

Derivative Property [Multiplied Constant]:
\displaystyle (cu)' = cu'

Derivative Property [Addition/Subtraction]:
\displaystyle (u + v)' = u' + v'

Derivative Rule [Basic Power Rule]:

  1. f(x) = cxⁿ
  2. f’(x) = c·nxⁿ⁻¹

Derivative Rule [Product Rule]:
\displaystyle (uv)' = u'v + uv'

Derivative Rule [Quotient Rule]:
\displaystyle \bigg( \frac{u}{v} \bigg)' = \frac{vu' - uv'}{v^2}

Derivative Rule [Chain Rule]:
\displaystyle [u(v)]' = u'(v)v'

Step-by-step explanation:

*Note:

Since the answering box is <em>way</em> too small for this problem, there will be limited explanation.

<u>Step 1: Define</u>

<em>Identify.</em>

\displaystyle y = \frac{\cos^2 x - 3\sqrt{x} +6}{\sin^2 x + 6} \times \frac{\tan^2 x + 5x}{\csc^2 x + 3}

<u>Step 2: Differentiate</u>

We can differentiate this function with the use of the given <em>derivative rules and properties</em>.

Applying Product Rule:

\displaystyle y' = \bigg( \frac{\cos^2 x - 3\sqrt{x} + 6}{\sin^2 x + 6} \bigg)' \frac{\tan^2 x + 5x}{\csc^2 x + 3} + \frac{\cos^2 x - 3\sqrt{x} +6}{\sin^2 x + 6} \bigg( \frac{\tan^2 x + 5x}{\csc^2 x + 3} \bigg) '

Differentiating the first portion using Quotient Rule:

\displaystyle \bigg( \frac{\cos^2 x - 3\sqrt{x} + 6}{\sin^2 x + 6} \bigg)' = \frac{\big( \cos^2 x - 3\sqrt{x} + 6 \big)' \big( \sin^2 x + 6 \big) - \big( \sin^2 x + 6 \big)' \big( \cos^2 x - 3\sqrt{x} + 6 \big)}{\big( \sin^2 x + 6 \big)^2}

Apply Derivative Rules and Properties, namely the Chain Rule:

\displaystyle \bigg( \frac{\cos^2 x - 3\sqrt{x} + 6}{\sin^2 x + 6} \bigg)' = \frac{\big( -2 \cos x \sin x - \frac{3}{2\sqrt{x}} \big) \big( \sin^2 x + 6 \big) - \big( 2 \sin x \cos x \big) \big( \cos^2 x - 3\sqrt{x} + 6 \big)}{\big( \sin^2 x + 6 \big)^2}

Differentiating the second portion using Quotient Rule again:

\displaystyle \bigg( \frac{\tan^2 x + 5x}{\csc^2 x + 3} \bigg) ' = \frac{\big( \tan^2 x + 5x \big)' \big( \csc^2 x + 3 \big) - \big( \csc^2 x + 3 \big)' \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big)^2}

Apply Derivative Rules and Properties, namely the Chain Rule again:
\displaystyle \bigg( \frac{\tan^2 x + 5x}{\csc^2 x + 3} \bigg) ' = \frac{\big( 2 \tan x \sec^2 x + 5 \big) \big( \csc^2 x + 3 \big) - \big( -2 \csc^2 x \cot x \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big)^2}

Substitute in derivatives:

\displaystyle y' = \frac{\big( -2 \cos x \sin x - \frac{3}{2\sqrt{x}} \big) \big( \sin^2 x + 6 \big) - \big( 2 \sin x \cos x \big) \big( \cos^2 x - 3\sqrt{x} + 6 \big)}{\big( \sin^2 x + 6 \big)^2} \frac{\tan^2 x + 5x}{\csc^2 x + 3} + \frac{\cos^2 x - 3\sqrt{x} +6}{\sin^2 x + 6} \frac{\big( 2 \tan x \sec^2 x + 5 \big) \big( \csc^2 x + 3 \big) - \big( -2 \csc^2 x \cot x \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big)^2}

Simplify:

\displaystyle y' = \frac{\big( \tan^2 x + 5x \big) \bigg[ \big( -2 \cos x \sin x - \frac{3}{2\sqrt{x}} \big) \big( \sin^2 x + 6 \big) - 2 \sin x \cos x \big( \cos^2 x - 3\sqrt{x} + 6 \big) \bigg]}{\big( \sin^2 x + 6 \big)^2 \big( \csc^2 x + 3 \big)} + \frac{\big( \cos^2 x - 3\sqrt{x} +6 \big) \bigg[ \big( 2 \tan x \sec^2 x + 5 \big) \big( \csc^2 x + 3 \big) + 2 \csc^2 x \cot x \big( \tan^2 x + 5x \big) \bigg] }{\big( \csc^2 x + 3 \big)^2 \big( \sin^2 x + 6 \big)}

We can rewrite the differential by factoring and common mathematical properties to obtain our final answer:

\displaystyle y' = \frac{\big( -2 \cos x \sin x - \frac{3}{2\sqrt{x}} \big) \big( \tan^2 x + 5x \big) + \big( \cos^2 x - 3\sqrt{x} + 6 \big) \big( 2 \sec^2 x \tan x + 5 \big)}{ \big( \csc^2 x + 3 \big) \big( \sin^2 x + 6 \big)} + \frac{2 \cot x \csc^2 x \big( \cos^2 x - 3\sqrt{x} + 6 \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big)^2 \big( \sin^2x + 6 \big)} - \frac{2 \cos x \sin x \big( \cos^2 x - 3\sqrt{x}  + 6 \big) \big( \tan^2 x + 5x \big)}{\big( \csc^2 x + 3 \big) \big( \sin^2 x + 6 \big)^2}

∴ we have found our derivative.

---

Learn more about derivatives: brainly.com/question/26836290

Learn more about calculus: brainly.com/question/23558817

---

Topic: Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

8 0
2 years ago
Read 2 more answers
A company provides a monthly pension to its employees. A person retiring at 62 retires and receives a full monthly pension. If t
IRISSAK [1]

Answer:

  • <em><u>The reduction is 8.6%</u></em>

Explanation:

Call F the full monthly pension of a person retiring at 62.

If a person continues to work the pension grows at a rate of 6% per year, compounded monthly, so use the compounded growing formula:

  • Pension=F(1+r/12)^{12t}

Where r = 6 / 100 = 0.06, and t = number of years after retirement.

<u>For retirement at 65.5</u>:

  • t = 65.5 - 62 = 3.5

  • Pension=F(1+0.06/12)^{12\times 3.5}=1.233F

<u>For retirement at 67</u>:

  • t = 67 - 62 = 5

  • Pension=F(1+0.06/12)^{12\times 5}=1.349F

<u>Percent reduction of people who retire at 65.5 compared to what they would receive at 67</u>:

  • (1.349F-1.233F)\times 100/(1.349F)=8.6\%
8 0
3 years ago
Express 4x^2-25 as a product of two binomials.
Andrei [34K]

4x^2-25= (2x)^2-5^2=(2x-5)(2x+5)

Used: a^2-b^2=(a+b)(a-b)

5 0
3 years ago
Read 2 more answers
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