Question

State whether there is a maximum or a minimum
f(x)=5-x^2+2x

Answer 1

differentiate with respective to x

f'(×)=-2x+2

f'(×) >0 for x<1

f'(X)<0 for x>1

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

Answer 2

maximum

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