Let 𝑓 be a function such that lim ℎ→0 𝑓(3+ℎ)−𝑓(3) / ℎ = 5. Which ones must be true?

Question

(a)𝑓 is continuous at 𝑥 = 3

(b) 𝑓 is differentiable at 𝑥 = 3

(c) The derivative of 𝑓 is continuous at 𝑥 = 3

(d) 𝑓 can be integrate at 𝑥 = 2

(e) The area under the curve 𝑓 around 𝑥 = 3 is 5

Answer 1

a,b,and c have to be true for g when x=3.

d and e involve integration. Integration requires an upper x-value and a lower boundary x-value. Since 3 is the only x-value given. No guesses about Integration cab be made.