MAT 1300 Midterm: TopicsMid1-1300

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1300
• Professor: Termeh Kousha

Document Summary

Find the tangent line of the function f (x) = q 2x+1. First, we nd the derivative of f : this can be done in two ways. f 0(x) = Alternatively rst write f (x) = q 2. Next, plug in x = 1 in f 0(x): Thus the tangent line at x = 1 of f has slope . Plug in x = 1 into f : Now we know that the tangent line has to have the form y = . = r 3 f (1) = r 2 1 + 1. Thus the tangent line has to pass through the point (1, 1). Therefore the tangent line has equation y = y = . 6 x + b 1 = . Using the de nition of derivative, nd the derivative of f (x) = (2x 1)2. X f (x + x) f (x) 4x + 1 5 = 4x2. 4x 4, while (2x + 2 x 1)2.