Answer
Critical Number: x = 1
Increasing on the interval (-$\infty$, 1)
Decreasing on the interval (1, $\infty$)
Relative maximum: (1, 5)
Work Step by Step
f(x) = $-2x^{2}$+4x+3
f'(x) = -4x+4
Critical Number: x = 1
Interval: $\infty$ < x < 1 and 1 < x < $\infty$
Test Values: x = 0; x = 2
x = 0
f'(0) = -4(0) +4
f'(0) = 4
Increasing on the interval (-$\infty$, 1)
x = 2
f'(2) = -4(2) + 4
f'(2) = -4
Decreasing on the interval (1, $\infty$)
Indicates there is a max.
f(1) = $-2(1)^{2}$ + 4(1) + 3
f(1) = -2 + 4 + 3
f(1) = 5
Relative maximum: (1, 5)
