D In the first two Questions we write the definition of f' (-1) where f(2) = 32 - 32 + 2. 8 D Question 1 1 pts We first find of(-1) =-1+3+2=4 of(-1) =1-3+2=0 of(-1) =-1-3-2=-6 of (-1) = -1-3+2=-2 of (-1) = 1+3+2=6 D Question 2 1 pts Now, by definition f (a) = lim f(ac) - f(a) we have x - a O f' (-1) = lim - 3x +2 - 6 -1 x - 1 O f' (-1) = lim 2 - 3x + 2 - 6 x - - 1 x+1 f' ( -1) = lim 2 2 - 3x +2 - 6 x+1 f' (-1) = lim 2 - 3x + 2+4 x - - 1 O f' (-1) = lim x2 - 3x + 2 + 6 = >- 1 x+1D The next two Questions are about the definition of derivative of f(x) = va + 7 in a = -3. D Question 3 1 pts First step is to find the value of the function in a point: of (-3) = V2 of(-3) = 1 of ( -3) = -2 of(-3) = 2 of(-3) = 4 D Question 4 1 pts Now, by definition f' (a) = lim flath) - f(a) we have h +0 h o f' (-3) = lim f( -3 + h) - f(-3) = lim V -3 + h+7+2 h-+0 h h-+0 h o f' (-3) = lim f (3 + h) - f(-3) - lim V3th+7-1 h-0 h h-+0 h of' (-3) = lim f ( -3 + h) - f(-3) -3+h+7-2 = lim h h-+0 h O f' (-3) = lim f (3 + h) - f(-3) = lim V3 th +7-2 h h-+0 h O f' (-3) = lim f ( -3 + h) - f(-3) V-3+h -2 = lim h-0 h h-+0 h