Calculating derivatives a.?? or the following functions, find f using the definition? f (x) = lim f(x+h)?f(x). h?0 h 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) = ;a =? 5 x

SOLUTION STEP 1 (a). Given f(x) = 1 . x 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 f (x) = lim h h0 f(x + h) = 1 x+h 1 1 xxh Thus f (x) = lim x+h x= lim x(x+h= lim h h0 h h0 h h0 hx(x+h) 1 1 = h0 x(x+h)= x2 STEP 2 (b). Determine an equation of the line tangent to the graph of f at (a, f(a)) ,{ie,(-5,f(-5))} for the given...