f (x) is continuous at x = 1 and x = 4
Since g(x) = |x| is a continuous function and In particular f is continuous at x = 1 and x = 4. f is clearly not differentiable atx = 4. Since g(x) = |x| is not differentiable at x = 0. Now
Hence f is not differentiable at x = 1.
Give a function g which has derivative g’(x) for all x satisfying g’(0) = 2 and g(x + y) = ey g(x) + ex g(y) for all x, y Ïµ R, g(5) = 32. The value ofg’(5) – 2e5 is