Show that the function f(x) = |x5| is not differentiable at 5. We have f(x) = |x - 51 = (x-5) -(x-5) if x ≥ 5 if x < 5. The right-hand limit is lim x-5+ f(x) - f(5) X-5 = 1 and the left-hand limit is lim f(x) - f(5) X-5- X-5 = 1 Since these limits are not equal, f'(5): = Find a formula for f' and sketch its graph. 1 if x > 5 f'(x) = -1 if x < 5 Tools No Solution lim x 5 f(x) - f(5) X-5 does not exist and f is not differentiable at 5. Actions 7 6 5 4 3 2 1 -6 -5 4 -3 -2 -1 2 3 5 6 2 -3 4 -5 6 7 Clear All A Delete Fill