Question

Найдите F(x)=5cos2x+2, если f(х)=π/3​

Answer 1

Ответ:

f (x) =5 cos^2 x

f ' (x) =5*2*cosx * (-sinx)

f ' (π/3) = 10*(1/2)*(-sqrt3/2)= - 5sqrt3/2

Пошаговое объяснение:

Answer 2

To find the value of F(x) given f(x) = π/3, we need to use the given expression for F(x) and substitute x with the value that corresponds to f(x) = π/3.

The given function is: F(x) = 5cos(2x) + 2

And we know that f(x) = π/3: f(x) = π/3

To find the value of x, we need to solve the equation for cos(2x) using the given value of f(x):

π/3 = 5cos(2x) + 2

Now, isolate cos(2x) on one side:

5cos(2x) = π/3 - 2

Next, divide by 5:

cos(2x) = (π/3 - 2) / 5

Now, we need to find the value of x such that cos(2x) is equal to ((π/3 - 2) / 5). To do this, we'll take the inverse cosine (arccos) of both sides:

2x = arccos((π/3 - 2) / 5)

Finally, divide by 2 to solve for x:

x = (1/2) * arccos((π/3 - 2) / 5)

Now, to find the value of F(x), substitute this value of x back into the expression for F(x):

F(x) = 5cos(2x) + 2

F(x) = 5cos(2 * ((1/2) * arccos((π/3 - 2) / 5))) + 2

F(x) = 5cos(arccos((π/3 - 2) / 5)) + 2

Since cos(arccos(u)) = u, we can simplify further:

F(x) = 5 * ((π/3 - 2) / 5) + 2

F(x) = π/3 - 2 + 2

F(x) = π/3

So, when f(x) = π/3, the value of F(x) is also π/3.