Question

Даны функции f(х)= 5х3+2х2-6х+7 и g(х)= 5х3. При каком значении х равны значения производных указанных функций?

Answer 1

F'(x) = 5*3*x^(3 -1) + 2*2*x^(2-1) - 6 = 15x^2 + 4x - 6
g'(x) = 5*3*x^(3-1) = 15x^2
15x^2 + 4x - 6 = 15x^2
4x - 6 = 0
4x = 6
x = 6/4 = 3/2 = 1,5
Ответ: при х = 1,5

Answer 2

To find the value(s) of x where the derivatives of the given functions are equal, we need to find when the derivatives of f(x) and g(x) are equal. The derivatives of the functions are as follows:

f'(x) = d/dx (5x^3 + 2x^2 - 6x + 7) f'(x) = 15x^2 + 4x - 6

g'(x) = d/dx (5x^3) g'(x) = 15x^2

Now, set f'(x) equal to g'(x) and solve for x:

15x^2 + 4x - 6 = 15x^2

Subtract 15x^2 from both sides:

4x - 6 = 0

Add 6 to both sides:

4x = 6

Divide both sides by 4:

x = 6/4

x = 3/2

So, the value of x at which the derivatives of f(x) and g(x) are equal is x = 3/2.