How to determine if a function is continuous and differentiable

🚀 What is Differentiability? The Idea Behind Derivatives! | Part 1

Let f: R → R be a differentiable function with f(0) = 0. If y = f(x) satisfies the differential

Q) Let 𝑓:[1,∞)→ℝ be a differentiable function, If 6∫_1^𝑥 𝑓(𝑡)𝑑𝑡=3𝑥𝑓(𝑥)+𝑥^3−4 for all x≥1,

Q) Let 𝑓:𝐑→𝐑 be a twice differentiable function such that 𝑓^′′ (x)=0 for all x∈𝐑 and

Q) Let 𝑓:[1,∞)→ℝ be a differentiable function, If 6∫1^𝑥 𝑓(𝑡)𝑑𝑡=3𝑥𝑓(𝑥)+𝑥^3−4 for a

Q) Let 𝑓:R→(0,∞) be a twice differentiable function such that f(3)=18,f^′ (3)=0 and f^′′ (3)=4.