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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)