Question

3) f(x)=x^(5/2)-x^(3/2) +7x-1, f'(2);​

Answer 1

Ответ: 2^5/2=4*корень из 2. 2^3/2=2*корень из 2.

Данное выражение перепишем как корень из 2*(4-2)+14-1=2*корень из 2+13.

Объяснение:

Answer 2

To find f'(x), the first derivative of f(x), we need to differentiate each term of the given function with respect to x and simplify:

f(x) = x^(5/2) - x^(3/2) + 7x - 1

f'(x) = (5/2)x^(3/2) - (3/2)x^(1/2) + 7

Now, we need to find f'(2), which means we need to substitute x=2 into f'(x):

f'(2) = (5/2)(2)^(3/2) - (3/2)(2)^(1/2) + 7

f'(2) = (5/2)(2*sqrt(2)) - (3/2)*sqrt(2) + 7

f'(2) = 5sqrt(2) - 3sqrt(2) + 7

f'(2) = 2sqrt(2) + 7

Therefore, f'(2) is equal to 2sqrt(2) + 7.