Write a sentence that correctly uses each of the following punctuation marks and/or parts of speech. a) semicolon (not in a list) b) colon c) comma with conjunction d) dialogue with marker
(Below are only examples; there are many "correct" answers, as a personal style may dictate usage of certain punctuation.) a) Semicolons are used to separate two closely related independent clauses; this means both clauses must have a subject and verb. b) I must tell you: colons are not difficult to use correctly in your writing, and will often add a bit of excitement to otherwise dull sentence structure. c) Commas should be used sparingly, but never forget to use them when necessary. d) Once we finished with the exercise, he told me, "I can't believe how easy that was!"
Given the function f(x) = x^3 + 6x^2 - 15x + 10, a) Give the first and second derivatives, b) Name the interval(s) on which the function is increasing, c) Name the interval(s) on which the function is concave up, and d) Name all local extrema and inflection points.
a) f'(x) = 3x^2 + 12x - 15 f''(x) = 6x + 12 b) increasing on intervals (-infinity, -5) and (1, infinity) c) concave up on interval (-2, infinity) d) local max at (-5, 110), local min at (1, 2), inflection point at (-2, 56)
Given the function f(x) = x^2 + 6x + 8, a) Write this function in factored form, b) Write this function in vertex from, c) Name the zeroes, and d) Name the vertex.
a) f(x) = (x + 4)(x + 2) b) f(x) = (x + 3)^2 - 1 c) x = -4, -2 (or) (-4,0),(-2,0) d) vertex is at (-3,-1)