Question

При каких значениях х производная от функции f(x) = -30 x2 + 85 x + 70 равна нулю

Answer 1

Найдём производную : 
f'(x)=-60x+85
-60x+85=0
x=85:60
x=85/60 или 17/12 (дроби)

Answer 2

To find the values of x for which the derivative of the function f(x) = -30x^2 + 85x + 70 is equal to zero, we need to find the critical points. Critical points are the values of x where the derivative is either zero or undefined.

Step 1: Find the derivative of f(x): f'(x) = d/dx (-30x^2 + 85x + 70)

To find the derivative of each term, apply the power rule: d/dx (-30x^2) = -30 * 2x^(2-1) = -60x d/dx (85x) = 85 * 1x^(1-1) = 85 d/dx (70) = 0 (constant term)

Now, combine the derivatives of the individual terms: f'(x) = -60x + 85

Step 2: Set the derivative equal to zero and solve for x: -60x + 85 = 0

Now, isolate x on one side of the equation: -60x = -85

Divide both sides by -60: x = -85 / -60

Simplify: x = 17/12

So, the derivative of the function f(x) is equal to zero when x = 17/12 or approximately 1.4167.