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} (d)/(dx)(x^n)=nx^(n-1) \\ \end{gathered}`

so:

`\begin{gathered} f(x)=3-5x \\ f(x)^(\prime)=(d)/(dx)(3)-(d)/(dx)(5x)=(d)/(dx)(3)-5(d)/(dx)(x) \\ so\colon \\ (d)/(dx)(3)=0 \\ (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)=(3)/(2)x+1 \\ g(x)^(\prime)=(3)/(2)=m \end{gathered}`