Question

Hey! I need help finding the slope of the Tangent at a given point as depicted in the following image: (Just need help with an explanation to #5)

Answer 1

5.

$\begin{gathered} \frac{d}{dx}(x^n)=nx^{n-1} \\ \end{gathered}$

so:

$\begin{gathered} f(x)=3-5x \\ f(x)^{\prime}=\frac{d}{dx}(3)-\frac{d}{dx}(5x)=\frac{d}{dx}(3)-5\frac{d}{dx}(x) \\ so\colon \\ \frac{d}{dx}(3)=0 \\ \frac{d}{dx}(x)=1x^{1-1}=1x^0=1\cdot1=1 \\ f(x)^{\prime}=0-5 \\ f(x)^{\prime}=-5 \end{gathered}$

6.

$\begin{gathered} g(x)=\frac{3}{2}x+1 \\ g(x)^{\prime}=\frac{3}{2}=m \end{gathered}$