please show all work hand-written

1.

1. Given the following information: f (2) = 5, f '(2) =4, f (5) =6, f '(5) = 7, find [f - ] (5) = ?2. The slope of the tangent line to the curve f(x) at (2,8) is 4. Given f(x) is invertible, find the equation of the tangent line to f 1(x) at x =8. 3. Are the following functions monotone and hence invertible? Verify your answer using calculus. You don't need to include the work here. (a) f ( x) =3x +4x+1 Yes or no: (b ) f ( x ) = 4 x - 5 x + 2 Yes or no: (c) f (x ) =x*+ 5x2 +2 Yes or no: (d) f (x) =5cos(2x) Yes or no: (e) f (x ) = Vx2 + 1 Yes or no: 1 ( f) f ( x) = Yes or no: x2 + 2 (g) f( x) = er+ Yes or no:4. Find the derivatives of the following functions:\f5. Find the slope of the tangent line to the following curve at x =1 . (2x+1)3\\)Uc4 + 2 x) =11] (x+ 5f