Question

differentiate the function.
g(x) = \frac{1}{4}x^{2}-4x + 11
g(x)=

Explanation:

Step1: Apply power - rule to $\frac{1}{4}x^{2}$

The power - rule states that if $y = ax^{n}$, then $y^\prime=anx^{n - 1}$. For $y=\frac{1}{4}x^{2}$, $a = \frac{1}{4}$ and $n = 2$. So the derivative of $\frac{1}{4}x^{2}$ is $\frac{1}{4}\times2x=\frac{1}{2}x$.

Step2: Apply power - rule to $-4x$

For $y=-4x$, $a=-4$ and $n = 1$. Using the power - rule $y^\prime=anx^{n - 1}$, we get $-4\times1\times x^{1 - 1}=-4$.

Step3: Derivative of a constant

The derivative of a constant $C$ (in this case $C = 11$) is $0$.

Step4: Combine the derivatives

$g^\prime(x)$ is the sum of the derivatives of each term. So $g^\prime(x)=\frac{1}{2}x-4 + 0$.

Answer:

$\frac{1}{2}x-4$