SOLVE WITH SOLUTION LIKE IN THE PICTURE

BASIC CALCULUS: PROBLEM SET 2 Relate the derivative of a function to the slope of the tangent line Example: Determine the equation of the tangent line to f (x) = x - 9 at (2,-5). Solution: First, determine the slope of the tangent line to the function f: m= lim -2-im--[-5 *-2 = lim 142 1-2 = lim 1-2 = lim x+ 2 = 2+2 =4 - slope Then, substitute in = 4 and (2,-5) = (x1. y,) to point-slope form: point-slope form: y - y = m(x - x;) y - (-5) = 4(x - 2) y + 5 =4x -8 y = 4x -8-5 y = 4x - 13 - equation of tangent line Determine the slope and equation of the tangent line to the following functions at the specified points. (3 pts each) 1) f(x) =3-Sx at (-1,8) 6) f(x) = Vx at (2.8) 2) f (x) = $x+1 at (-2,-2) 7) f (x) = Vx2-1 at (5,2) 3) ((1) =13+3 at (-2,7) 8) g(x) = x+= at (4.5) 4) g(x) = x2 -6 at (1,5) 9) ((x ) = - VI+ 1 at (1,4) 5) 9(h) = 3h -h> at (0,0) 10) g(h) = = + 1 at (0,1)