Question

F(x)=x² +6

Find an equation for the tangent line to the graph of f(x) = x² +6 at (5,31).
y=

Answer 1

y = x^2 + 6 given equation

y = m x + b equation of straight line required

dy/dx = 2 x tangent to given curve

dy/dx = slope = 2 * 5 = 10

Thus our line must be of the form

y = 10 x + b

31 = 10 * 5 + b at the point required

b = 31 - 50 = -19

Then our final equation becomes

y = 10 x - 19