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Olenka [21]
3 years ago
14

Ex 2.8 3. find the maximum value of y for the curve y=x^5 -3 for -2≤x≤1

Mathematics
1 answer:
harkovskaia [24]3 years ago
4 0
y=x^5-3\\ y'=5x^4\\\\ 5x^4=0\\ x=0\\ 0\in [-2,1]\\\\ y''=20x^3\\\\
y''(0)=20\cdot0^3=0

The value of the second derivative for x=0 is neither positive nor negative, so you can't tell whether this point is a minimum or a maximum. You need to check the values of the first derivative around the point.
But the value of 5x^4 is always positive for x\in\mathbb{R}\setminus \{0\}. That means at x=0 there's neither minimum nor maximum.
The maximum must be then at either of the endpoints of the interval [-2,1].
The function y is increasing in its entire domain, so the maximum value is at the right endpoint of the interval.

y_{max}=y(1)=1^5-3=-2
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Now you can form an equation.

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5(8k + 9m) simplified expression
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3 years ago
#Quality answer needed <br>#No spam _/|\_​
Rina8888 [55]

Answer:

<h2><em><u>5.71</u></em><em><u>%</u></em></h2>

Step-by-step explanation:

<em><u>Given</u></em><em><u>,</u></em>

Cost price of the car when Arjun bought = ₹ 3,50,000

Cost price of that same car after 1 year = ₹ 3,70,000

<em><u>So</u></em><em><u>,</u></em>

Amount of money increased on the car's price

= ₹ (3,70,000 - 3,50,000)

= ₹ 20,000

<em><u>Therefore</u></em><em><u>,</u></em><em><u> </u></em>

Percentage of increase on the car's price

=  \frac{20000}{350000}  \times 100

  • <em>[</em><em>On</em><em> </em><em>Simplification</em><em>]</em>

=  \frac{2}{35}  \times 100

  • <em>[</em><em>On</em><em> </em><em>further</em><em> </em><em>Simplification</em><em>]</em>

= 5.7142......

= 5.71 (approx.)

<em><u>Hence</u></em><em><u>,</u></em>

<em><u>Percentage</u></em><em><u> </u></em><em><u>in</u></em><em><u> </u></em><em><u>increase</u></em><em><u> </u></em><em><u>of</u></em><em><u> </u></em><em><u>car's</u></em><em><u> </u></em><em><u>price</u></em><em><u> </u></em><em><u>was</u></em><em><u> </u></em><em><u>5.71</u></em><em><u>%</u></em><em><u> </u></em><em><u>(</u></em><em><u>Ans</u></em><em><u>)</u></em>

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2 years ago
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