Question

Urgent - Calculus - Find the absolute maximum value and the absolute minimum value, if any, of the function. (If an answer does not exist, enter DNE.)

f(x) = x^2 − x − 4 on [0, 4]

Answer 1

Explanation:

The graph of f(x) = x^2 − x − 4 is that of a parabola that opens upward and whose axis of symmetry is given by x = -b/(2a), where here a = 1 and b = -1:

-1

x = - --------- = 1. This x = 1 is also the x-coordinate of the vertex, and the

2(`1) axis of symmetry passes vertically through (1, 1^2 - 1 -4),

(or 1, -4).

The largest y value possible on the interval [0, 4] is f(4) = 4^2 - 4 - 4, or 8, or (4, 8). This is the absolute maximum value of f(x) on the interval [0, 4].

The absolute minimum value is the v-value at the vertex: (1, -4)