Question

F'(0,5) если f(x)=x^3+9x^2-x+2

Answer 1

Ответ:

надо сначала возвести все что есть в степени ,потом перемножить 9 на получившееся число в квадрате ,и в конце сложить

Answer 2

To find the derivative of the function $f(x)=x^3+9x^2-x+2$ and then evaluate it at $x=0.5$, we can follow these steps:

Step 1: Find the derivative $f'(x)$ of the function $f(x)$ with respect to $x$. Step 2: Substitute $x=0.5$ into the derivative $f'(x)$ to find the value at $x=0.5$.

Step 1: Find $f'(x)$: To find the derivative of $f(x)$, we can use the power rule. The power rule states that if $f(x) = x^n$, then $f'(x) = n \cdot x^{n-1}$. Applying the power rule to each term of $f(x)$:

$f'(x) = \frac{d}{dx}(x^3) + \frac{d}{dx}(9x^2) - \frac{d}{dx}(x) + \frac{d}{dx}(2)$

$f'(x) = 3x^2 + 18x - 1$

Step 2: Evaluate at $x=0.5$: Now, we substitute $x=0.5$ into $f'(x)$ to find the value of the derivative at $x=0.5$:

$f'(0.5) = 3(0.5)^2 + 18(0.5) - 1$

$f'(0.5) = 3(0.25) + 9 - 1$

$f'(0.5) = 0.75 + 9 - 1$

$f'(0.5) = 8.75$

So, $f'(0.5) = 8.75$.