For the following equation, evaluate f^(')(5). f(x)=4x^(2)+3x Answer:

Identify Function: Identify the function to differentiate. We are given the function f(x) = 4x^2 + 3x and we need to find its derivative, denoted by f'(x).Differentiate Function: Differentiate the function f(x) with respect to x. To find f'(x), we use the power rule for differentiation, which states that the derivative of x^n with respect to x is n*x^(n-1). Differentiating 4x^2 with respect to x gives us 2*4x^(2-1) = 8x. Differentiating 3x with respect to x gives us 3. So, f'(x) = 8x + 3.Evaluate Derivative: Evaluate the derivative at x = 5. We substitute x = 5 into the derivative f'(x) to find f'(5). f'(5) = 8(5) + 3 = 40 + 3 = 43.

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For the following equation, evaluate
f^(')(5).

f(x)=4x^(2)+3x
Answer:

For the following equation, evaluate $f^{\prime}(5)$ . $\newline$ $f(x)=4 x^{2}+3 x$ $\newline$ Answer:

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Algebra 2

Composition of linear and quadratic functions: find a value

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Q. For the following equation, evaluate

f^{\prime}(5)

\newline

f(x)=4 x^{2}+3 x

\newline

Answer:

Identify Function: Identify the function to differentiate. $\newline$ We are given the function $f(x) = 4x^2 + 3x$ and we need to find its derivative, denoted by $f'(x)$ .
Differentiate Function: Differentiate the function $f(x)$ with respect to $x$ . To find $f'(x)$ , we use the power rule for differentiation, which states that the derivative of $x^n$ with respect to $x$ is $n\cdot x^{(n-1)}$ . Differentiating $4x^2$ with respect to $x$ gives us $2\cdot 4x^{(2-1)} = 8x$ . Differentiating $3x$ with respect to $x$ gives us $x$ $1$ . So, $x$ $2$ .
Evaluate Derivative: Evaluate the derivative at $x = 5$ . $\newline$ We substitute $x = 5$ into the derivative $f'(x)$ to find $f'(5)$ . $\newline$ $f'(5) = 8(5) + 3 = 40 + 3 = 43$ .