Question

How would I write an equation for this tangent line, g(3)=6 , g'(3)=-2

Answer 1

g(3)=6 means that when x = 3, y = 6

So the point (3,6) lies on the curve

g(3) = -2 means that on the curve at x = 3, the tangent line has a slope of m = -2


So use the point slope formula

y-y1 = m(x-x1)


and plug these values in to get


y-6 = -2(x-3)


From here, solve for y to find the equation for the tangent line