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

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

f (x) = x3 − x, [0, 2].Determine a number c ∈ (0, 2) that satisfy the conclusions of the MVT

Suppose that f : [0, 4] → R is continuous on [0, 4], is differentiable on (0, 4) and thatf (0) = 0, f (1) = 3, f (4) = −3.Show that there exists c ∈ (0, 4) such that f ′(c) = −1

Let g:R→R be a non constant twice differentiable such that g′(12)=g′(32). If a real valued function f is defined as f(x)=12[g(x)+g(2−x)], thenf′′(x)=0 for atleast two x in (0,2)f′′(x)=0 for exactly one x in (0,1)f′′(x)=0 for no x in (0,1)f′(32)+f′(12)=1

Consider the function h(x)=sin(2x)+cos(x2)+ex3ℎ(𝑥)=sin⁡(2𝑥)+cos⁡(𝑥2)+𝑒𝑥3. Then h′(0)=ℎ′(0)= Answer 1 Question 3.