If you help ill give you some of my banana milk...
1 answer:
Given:
The function is:
To find:
The domain of the given function.
Solution:
Domain is the set of input values.
We have,
It is a quadratic polynomial.
We know that a quadratic polynomial is defined for all real values of x. So, the given function is defined for all real values of x and the domain of the given function is:
Domain = Set of all real number
Domain = (-∞,∞)
Therefore, the correct option is B.
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The maxima of f(x) occur at its critical points, where f '(x) is zero or undefined. We're given f '(x) is continuous, so we only care about the first case. Looking at the plot, we see that f '(x) = 0 when x = -4, x = 0, and x = 5.
Notice that f '(x) ≥ 0 for all x in the interval [0, 5]. This means f(x) is strictly increasing, and so the absolute maximum of f(x) over [0, 5] occurs at x = 5.
By the fundamental theorem of calculus,
The definite integral corresponds to the area of a trapezoid with height 2 and "bases" of length 5 and 2, so