f(c) is the maximum value of f on [a, b] if 𝑓(𝑐)≤𝑓(𝑥)

Identify the statement that is FALSE:If a function 𝑓 is continuous on (𝑎,𝑏), then 𝑓 always has an absolute minimum on (𝑎,𝑏).If a function 𝑓 is continuous on [𝑎,𝑏], then 𝑓 always has an absolute minimum on [𝑎,𝑏].If a function 𝑓 is continuous on [𝑎,𝑏] and 𝑓 has no relative extrema in (𝑎,𝑏), then the absolute maximum of 𝑓 on [𝑎,𝑏] exists and occurs at either 𝑥=𝑎 or 𝑥=𝑏.If a function 𝑓 has an absolute minimum value on (𝑎,𝑏), then there is a critical point of 𝑓 in (𝑎,𝑏).

For f:(a,b]→R𝑓:(𝑎,𝑏]→𝑅, f(x)=10−x𝑓(𝑥)=10−𝑥 where a<b𝑎<𝑏, the range is

Consider the function:𝑓(𝑥)=𝑥3−3𝑥22−36𝑥Find the relative maximum point on this function.

Let 𝑓(𝑥)=𝑥3−3𝑥2+2𝑥f(x)=x 3 −3x 2 +2x. Find the maximum and minimum values of the function 𝑓(𝑥)f(x) on the interval [0,3][0,3].

Problem 4. Define the function f : R → R by f (x) = max{0, x}. For each a ∈ R, determineif f is differentiable at a and prove your answer