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

Find Derivative: First, we need to find the derivative of the function f(x) = -3x^2 + 4x. The derivative of a function gives us the rate at which the function's value changes at any given point. To find the derivative, we will use the power rule, which states that the derivative of x^n is n*x^(n-1).Apply Power Rule: Using the power rule, the derivative of -3x^2 is -3 * 2x^(2-1) = -6x. Similarly, the derivative of 4x is 4 * 1x^(1-1) = 4. Therefore, the derivative of the function f(x) = -3x^2 + 4x is f'(x) = -6x + 4.Evaluate at x = -3: Now that we have the derivative f'(x) = -6x + 4, we need to evaluate it at x = -3. This means we will substitute -3 for x in the derivative and simplify.Substitute in Derivative: Substituting -3 into the derivative, we get f'(-3) = -6(-3) + 4. Now we will perform the multiplication and addition to find the value.Calculate Rate of Change: Calculating f'(-3) gives us f'(-3) = -6(-3) + 4 = 18 + 4 = 22. This is the rate of change of the function f(x) at x = -3.

Home

Math Problems

Algebra 2

Evaluate expression when a complex numbers and a variable term is given

Full solution

Q. For the following equation, evaluate

f^{\prime}(-3)

\newline

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

\newline

Answer:

Find Derivative: First, we need to find the derivative of the function $f(x) = -3x^2 + 4x$ . The derivative of a function gives us the rate at which the function's value changes at any given point. To find the derivative, we will use the power rule, which states that the derivative of $x^n$ is $n\cdot x^{(n-1)}$ .
Apply Power Rule: Using the power rule, the derivative of $-3x^2$ is $-3 \times 2x^{2-1} = -6x$ . Similarly, the derivative of $4x$ is $4 \times 1x^{1-1} = 4$ . Therefore, the derivative of the function $f(x) = -3x^2 + 4x$ is $f'(x) = -6x + 4$ .
Evaluate at $x = -3$ : Now that we have the derivative $f'(x) = -6x + 4$ , we need to evaluate it at $x = -3$ . This means we will substitute $-3$ for $x$ in the derivative and simplify.
Substitute in Derivative: Substituting $-3$ into the derivative, we get $f'(-3) = -6(-3) + 4$ . Now we will perform the multiplication and addition to find the value.
Calculate Rate of Change: Calculating $f'(-3)$ gives us $f'(-3) = -6(-3) + 4 = 18 + 4 = 22$ . This is the rate of change of the function $f(x)$ at $x = -3$ .