Question

Решите уравнение f'(x)=g'(x),если f (x)=x^3/3 и g (x)=3x^2-9x+7

Answer 1

F'(x)=x^2
g'(x)=6x-9
x^2=6x-9
x^2-6x+9=0
(x-3)^2=0
x-3=0
x=3

Answer 2

To solve the equation f'(x) = g'(x), we need to find the first derivatives of both functions f(x) and g(x) and then equate them.

Given: f(x) = x^3/3 g(x) = 3x^2 - 9x + 7

First, let's find the first derivatives of f(x) and g(x):

f'(x) = d/dx(x^3/3) = x^2

g'(x) = d/dx(3x^2 - 9x + 7) = 6x - 9

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

x^2 = 6x - 9

To solve this quadratic equation, let's move all terms to one side and set the equation equal to zero:

x^2 - 6x + 9 = 0

Now, factor the quadratic equation:

(x - 3)(x - 3) = 0

(x - 3)^2 = 0

To find the solutions for x, set each factor to zero and solve for x:

x - 3 = 0

x = 3

So, the solution to the equation f'(x) = g'(x) is x = 3.