State whether there is a maximum or a minimum

f (x) = 5-x^2+2x

maximum

Step-by-step explanation:

Given a quadratic in standard form

y = ax² + bx + c (a ≠ 0), then

• If a > 0 then minimum value

• If a < 0 then maximum value

Given

f (x) = 5 - x² + 2x = - x² + 2x + 5 ← in standard form

with a = - 1 < 0

Thus f (x) has a maximum value

differentiate with respective to x

f' (*) = -2x+2

f' (*) >0 for x<1

f' (X) 1

therefore the function keeps increasing from - infinty to 1 and starts decreasing from 1to + infinity. ie the graph has a maximum