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

Given the functionf(x)=−5x2−x+20f(x) = −5x^2 − x + 20f(x)=−5x2−x+20, findf(3)f(3)f(3).

for each case, find the ARC over the given interval. a) f(x) = x^4 - x^3 + x^2, [-1,1] b) f(x) = (2x - 1)/(2x + 1), [0,2]

Let f and g be two twice differentiable functions defined form R → R. If f (x) has a local maximum at x = c and g(x) has a local minimum at x = c, then*

Let p ∈ Q. Define f (x) = xp for x > 0. Prove that f is differentiable on (0, ∞) and thatf ′(x) = pxp−1 for all x > 0