F(x) = x - 2sinx
To find for what values of x graph has tangents we need to differentiate function f(x).
f'(x) = 1-2cosx
Now, if we want to have horizontal tangents we need to make function f'(x) equal to 0 because at minimum or maximum of function f(x) tangent is horizontal.
1-2cosx = 0
cosx = 1/2
x = pi/3 + 2*n*pi and
x = -pi/3 + 2*n*pi
Explanation: cosx = 1/2 for both 60° and -60°. If we make one circle cosx will be equal to 1/2 for 420 and 300 degrees. Writing degrees in radians (using pi) we can write formulas above where 2*pi represents one full circle and n is an integer which represents how many circles we made.
<h3><u>Question:</u><u>-</u></h3>
A coca cola costs 150 yen. You buyed 30 bottles of cola and sold them at the price of 155 yen each. Find profit %
<h3><u>Answer</u><u>:</u><u>-</u></h3>
3.33%
<h3><u>Explanation</u><u>:</u><u>-</u></h3>
Cost price = ¥150
Selling price = ¥155
Total profit = Selling price - Cost price
→ = ¥155 - ¥150
→ = ¥5
Profit % = Profit × 100/cost price
️ = 5 × 100/150
️ = 10/3 = 3.33%
The average speed of Joshua during that time is 2500 m/h.
Explanation:
It is given that Joshua started cycling at 5:15 pm. By 8:09 pm he has covered a distance of 7250 m.
The total time taken by Joshua from 5:15 pm to 8:09 pm is
Dividing we get,
Adding, we have,
Thus, the total time taken by Joshua is 
To determine the average speed we use the formula,
where 
and 
Hence, substituting the values we have,
Dividing, we get,
Thus, the average speed of Joshua during that time is 2500 m/h.
