BASIC CALCULUS ( 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 -= 1im -9-[-5 *-2 = lim 1-2 = lim (*))(x-2) 1-2 = lim x + 2 = 2+2 =4 - slope Then, substitute in = 4 and (2, -5) = (x,. 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) 61 f(x) = Vx at (2,8) 2) ((x) = =x+ 1 at (-2,-2) 7) f(x) = Vx2-1 at (5,2) 3) f(1) =13+3 at (-2,7) B) g(x) = x+- at (4,5) 4) g(x) = x3 -6 at (1,5) 9) ( (x) = = Vx+ 1 at (1.4) 5) 9(h) = 3h - hi at (0,0) 10) 9(h) = = +1 at (0,1)