Q1)
Q2) Let f(x) = k^2 sin^2(2x) + bx, where x ε R and k, b are non zero
constants
a) Find f’(x)
b) For x ε R, the minimum value of sin(2x)cos(2x) is
Q3) <attached image>
Since , for all , we have .1. If , find .
Then using the chain-rule we find .
Write it as . Then (again) by the chain-rule,2. Let , where and k, b are non-zero constants.
Note that it's equavalent to - hence and . Then3. For , find the minimum value of .
we have . Recall that a minimum of is a point such that
and . Take the first zero of , that is , and we have ,
so it is a minimum. Thus the minimum value of is .
By the chain-rule (again) the derivative of [tex]e^{\frac{x}{3}}[/Math] is (fill the details). Since for any4. Find if
positive real , we have and the derivative of that is
(obviously) . Thus . (It's late over here so I apologise if there happen to be any
'mistypes' or mistakes).