78. G ( x ) = − x 4 + 32 x 2 + 144 (a) Determine whether G is even, odd, or neither. (b) There is a local maximum value of 400 at x = 4 . Determine a second local maximum value. (c) Suppose the area under the graph of G between x = 0 and x = 6 that is bounded from below by the x -axis axis is 1612.8 square units. Using the result from part (a), determine the area under the graph of G between x = − 6 and x = 0 that is bounded from below by the x -axis .
78. G ( x ) = − x 4 + 32 x 2 + 144 (a) Determine whether G is even, odd, or neither. (b) There is a local maximum value of 400 at x = 4 . Determine a second local maximum value. (c) Suppose the area under the graph of G between x = 0 and x = 6 that is bounded from below by the x -axis axis is 1612.8 square units. Using the result from part (a), determine the area under the graph of G between x = − 6 and x = 0 that is bounded from below by the x -axis .
Solution Summary: The author explains that the given function G is an even function.
(b) There is a local maximum value of 400 at
. Determine a second local maximum value.
(c) Suppose the area under the graph of G between
and
that is bounded from below by the
axis is 1612.8 square units. Using the result from part (a), determine the area under the graph of G between
and
that is bounded from below by the
.
Formula Formula A function f(x) attains a local maximum at x=a , if there exists a neighborhood (a−δ,a+δ) of a such that, f(x)<f(a), ∀ x∈(a−δ,a+δ),x≠a f(x)−f(a)<0, ∀ x∈(a−δ,a+δ),x≠a In such case, f(a) attains a local maximum value f(x) at x=a .
Find the absolute maximum of h(x)=x^2−x−2 over [−3,6].
What is meant by absolute, relative, percentage and round-off errors?If in the formula , the percentage error in R is not to exceed 0.3%, find the allowable percentage errors in r and h when r = 48 mm and h = 56 mm. In the evaluation of x4 - 3.17x3 + 5.29x - 1.173 at x = 5.12. Estimate the maximum rror assuming that all decimals are subject to maximum rounding off error.
In Exercises 1–4, use finite approximations to estimate the area under the graph of the function using a. a lower sum with two rectangles of equal width. b. a lower sum with four rectangles of equal width. c. an upper sum with two rectangles of equal width. d. an upper sum with four rectangles of equal width.
1. ƒ(x) = x2 between x = 0 and x = 1.
2. ƒ(x) = x3 between x = 0 and x = 1.
3. ƒ(x) = 1/x between x = 1 and x = 5.
4. ƒ(x) = 4 - x2 between x = -2 and x = 2.
University Calculus: Early Transcendentals, Single Variable (3rd Edition)
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