Question

F(x)= -2x^3+3x^2+5 (-2; 1) найти наибольшее значение функции

Answer 1

Ответ:

Пошаговое объяснение:

Answer 2

To find the maximum value of the function $F(x) = -2x^3 + 3x^2 + 5$ over the interval, we need to first determine the critical points of the function. Critical points occur where the derivative of the function is equal to zero or undefined.

Step 1: Find the derivative of $F(x)$: $F'(x) = d/dx(-2x^3 + 3x^2 + 5) = -6x^2 + 6x$.

Step 2: Set the derivative equal to zero and solve for $x$ to find the critical points: $-6x^2 + 6x = 0$. Factoring out $-6x$, we get $-6x(x - 1) = 0$. Setting each factor to zero and solving for $x$, we get $x = 0$ and $x = 1$.

Step 3: Determine the value of the function at the critical points and endpoints.

• $F(0) = -2(0)^3 + 3(0)^2 + 5 = 5$.
• $F(1) = -2(1)^3 + 3(1)^2 + 5 = 6$.
• $F(-2) = -2(-2)^3 + 3(-2)^2 + 5 = -24 + 12 + 5 = -7$.

Step 4: Compare the values obtained in Step 3 to find the maximum value of the function: The maximum value of the function is $6$ at the point $(1, 6)$.