Sketch the graph of f and use your sketch to find the absolute and local maximum and minimum values of f.

Question

Sketch the graph of f and use your sketch to find the absolute and local maximum and minimum values of f.

f(x) = 3 - x

Find the absolute maximum value. [ Enter your answers as a comma-separated list. i.e. (x,y) If an answer does not exist, enter DNE.]

Answer 1

f(x) = 3 -sqrx is y= -sqrx shifted up 3 units

square both sides

y^2 = x is a rightward opening parabola with vertex at the origin

but y=-sqrx is just the lower half of that parabola

with maximum at the origin. Shift it up 3 and the absolute maximum is y=3 or the point (0,3)

the answer you got on Desmos was right

that's an absolute and local maximum

there are no absolute minimums, local or global.

the minimum approaches negative infinity