Answer to Question #1703 in Calculus for Natalia

Question

Suppose k '(1) = 2.
(a) If f(x) = k(5x), find f '(1/5).
(b) If g(x) = k(x+ 2), find g '(-1).
(c) If h(x) = k(x / 7), find h '(7).

Answer 1

(a) If f(x) = k(5x) then f'(x) = 5 k'(5x), f'(1/5) = 5 k'(5*1/5) = 5;
(b) If g(x) = k(x +2) then g'(x) = k'(x+2),& g'(x) = k'(-1 +2) = 1;
(c) If h(x) = k(x/7) then h'(x) = 1/7 k'(x/7), h'(x) = 1/7 k'(7/7) = 1/7.