Let h(x)=min{x, x2}, ∀ x∈R, then -h(x) is not differentiable at two values of xh(x) is differentiable ∀ x∈Rh′(x)>0, ∀ x>1None of these

Let f, g : R → R be differentiable on [1, 2]. Suppose that f (1) = g(1) − 1 andf ′(x) ≤ g′(x) − 1 for all x ∈ [1, 2].Prove thatg(2) ≥ f (2) + 2.Hint) Consider the function h(x) := g(x) − x − f (x). Prove that h is non-negative on [1, 2

Find the 𝑥-values of both critical points of the following function. Then use the first derivative test to classify each of them as either a relative minimum, relative maximum, or neither.𝑦=−𝑥33−𝑥22+30𝑥−8 Find the first derivative.𝑦′=

Let f(x) be a differentiable function in the interval (0,2), then the value of ∫20f(x)dxf(c) where c∈(0,2)2f(c) where c∈(0,2)f′(c) where c∈(0,2)None of these

Use the first derivative test to find the two critical points of the function. First point:(Either of the points can be 𝑥1 or 𝑥2.)𝑥1= Relative Maximum Relative Minimum Neither

Let f(x) be a differentiable function in the interval (0,2), then the value of ∫20f(x)dx