Answer:
The turns of a graph is represented by the number of maximum or minimum that the function has.
If we differenciate f(x) we get:
f'(x)=4x^3+6x
f'(x)=2x(2x^2 + 3)
Therefore f'(x) =0, when x=0. Given that negative roots are not defined.
Therefore, the number of turns will be given by the number of solutions of f'(x) which is 1.
Attached you find the graph of the function which confirms the number of turns.
If the function had other solutions, the maximum number of turns it could have is 3! because f'(x) is a third degree polynomial, therefore it can't have more than 3 solutions!
Answer:
The square root of 33 is 5.74456264654
9514 1404 393
Answer:
- (c1, c2, c3) = (-2t, 4t, t) . . . . for any value of t
- NOT linearly independent
Step-by-step explanation:
We want ...
c1·f1(x) +c2·f2(x) +c3·f3(x) = g(x) ≡ 0
Substituting for the fn function values, we have ...
c1·x +c2·x² +c3·(2x -4x²) ≡ 0
This resolves to two equations:
x(c1 +2c3) = 0
x²(c2 -4c3) = 0
These have an infinite set of solutions:
c1 = -2c3
c2 = 4c3
Then for any parameter t, including the "trivial" t=0, ...
(c1, c2, c3) = (-2t, 4t, t)
__
f1, f2, f3 are NOT linearly independent. (If they were, there would be only one solution making g(x) ≡ 0.)
Answer:
the present value is 3,162 euros
Step-by-step explanation:
The computation of the present value is shown below:
As we know that
Future value = Present value × (1 + rate of interest)^number of years
3,200 euros = Present value × (1 + 0.012)^1
3,200 euros = Present value × 1.012^1
Present value is
= 3,200 euros ÷ 1.012
= 3,162 euros
Hence, the present value is 3,162 euros
20 mysteries. Add 20% and 30% to get 50%. Then rewrite 50% as 50/100. Next multiply 50/100 by 40 to get 2,000/100.The last thing to do is simplify to get 20 and subtract 20 from 40 to get 20 mysteries.
