Let $\displaystyle g(x) = x^2-3x+4$

a. Find the average rate of change of $\displaystyle g$ over the interval $\displaystyle [1,4]$

b. Find the rate of change of $\displaystyle g$ at $\displaystyle x=3$

c. Find the equation of the tangent line at $\displaystyle x=3$

d. Find the equation of the normal line at $\displaystyle x=3$

Here are my answers, are they correct?

a. 2

b. 3

c. $\displaystyle y-4=3(x-3)$

d. $\displaystyle y-4=-\frac{1}{3}(x-3)$