Solution for (a)
f(x) = 4 - x + x^2
Local extrema is where f'(x) = 0
f'(x) = 2x - 1 = 0, x = 0.5
f(x) = 4 - 0.5 + 0.5^2 = 3.75
Now use a graphing calculator to see how the graph behaves.
The results are that f(x) has a local minimum at (0.500,3.750)
Solution for (b):
g(x) = x³ - 4x + 1
g'(x) = 3x² - 4 = 0
x² = 4/3 , x ≈ + or - 1.155
When x is 1.155;
g(x) = 1.155³ - 4(1.155) + 1 ≈ -2.079
When x is -1.155;
g(x) = -1.155³ + 4(1.155) + 1 ≈ 4.079
Local maximum is at (-1.155,4.079)
Local minimum is at (1.155,-2.079)
