Calculating derivatives f(x+h)?f(x) a.?? or the following functions, find f using the definition? f (x) = lim h . h?0 b.? ?Determine an equation of the line tangent to the graph of f at? (?a?, ?f?(?a?)) ?for the given value of a. f(x) = x + 2; a = 7

SOLUTION STEP 1 (a). Given f(x) = x+2. We need to find the derivative of f(x) using the definition of the derivative f(x+h)f(x) The definition of the derivative is(x) = lim h h0 f(x+h) = (+h)+2 (x+h)+2 x+2 Thus f (x) =h0m h To solve this we have to multiply the numerator and the denominator with the conjugate of the numerator. (x+h)+2 x+2 (x+h)+2 x+2 (x+h)+2+ x+2 Therefore f(x) = lim h = lim h × (x+h)+2+ x+2 h0 h0 =lim (x+h)+2(x+2)= lim h = h0 h (x+h)+2+ x+2 h0 h (x+h)+2+ x+2 = 1 = 1 x+2+ x+2 2 x+2 Therefore...