Logan B. answered • 06/08/20

Intuitive Mathematics Instructor Focused on Advanced Mathematics

(1) True. Differentiation is linear, so (f+g)'(x) = f'(x) + g'(x). Hence, (f+g)'(5) = f'(5) +g'(5) = 1.8 + 4.2 = 6.

(2) True. Take, for instance, f(x) = x^{1/3}. Then (0, 0) is an inflection point, but f'(0) is undefined.

(3) False. Consider f(x) = (3/4) * x^{4/3}. Then f'(x) = x^{1/3} is defined everywhere, but f''(x) = (1/3) * x^{-2/3} is undefined at x=0.