SOLUTION: Determine the general equation of the scant from any point ( A,f(A) to the point on f(x)= 4^x where x=2. Describe how you would use this to find the equation of the tangent at the

Algebra ->  Linear-equations -> SOLUTION: Determine the general equation of the scant from any point ( A,f(A) to the point on f(x)= 4^x where x=2. Describe how you would use this to find the equation of the tangent at the      Log On


   

Question 840164: Determine the general equation of the scant from any point ( A,f(A) to the point on f(x)= 4^x where x=2. Describe how you would use this to find the equation of the tangent at the point (2, f(2))
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The line passes through two points (2, 16) and (x, 4^x). Find the slope of the line between these two points, and then find the equation of the line using point-slope form.

To find the equation of the tangent at (2, 16), let (x, 4^x) get arbitrarily close to (2, 16). Note that f'(x) = 4^x ln 4, and f'(2) = 16 ln 4.