Concept explainers
Graphical Reasoning Consider the function
(a) Use a graphing utility to graph the function and estimate the values of
(b) Use your results from part (a) to determine the values of
(c) Sketch a possible graph of f'
(d) Use the definition of derivative to find f'(x).
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Calculus: Early Transcendental Functions
- Find the area of a triangle bounded by the y axis, the line 2 f(x) 6 - x, and the line perpendicular to f(x) that 3 passes through the origin. Areaarrow_forwardUsing the graphing utility, graph the function y = f'(x). f'(x) = x – 16x³ + 81x? – 146x + 80 f' (x) = ,4 – 16x³ + 81x? - 146x + 80 40 y + 20 -2 4 10 -20 --40 -60 -80 powered by desmos -100 Use the graph to find the point(s) of inflection of f. (Give your answer in the form of a comma-separated list of values. Express numbers in exact form. Use symbolic notation and fractions where needed. Enter DNE if the function has no inflection points.) Use the graph to determine the interval(s) on which the function f is concave down. (Give your answer as an interval in the form (*, *). Use the symbol o for infinity, U for combining intervals, and an appropriate type of parenthesis "(",")", "[","]" depending on whether the interval is open or closed. Enter Ø if the interval is empty. Use decimal notation. Give your numbers to three decimal places.) interval(s):arrow_forwardUsing the graphing utility, graph the function y = f'(x). f'(x) = x* – 15x³ + 73x² – 129x + 70 f'(x) = y -400 200 -40 -20 20 40 --200- -400 powered by desmos -600 +arrow_forward
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- Differentiate. f(x) = excosxarrow_forward4 The functions f and g are defined as f(x) = 1 g(x) = 6-x X+7' a) Find the domain of f, g, f+ g, f-g, fg, f, and b) Find (f+ g)(x), (f- g)(x), (fg)(x), (ff)(x), (x), and (x). a) The domain of f is (Type your answer in interval notation.)arrow_forwardEquation Original Function f(x) = (x + 6)², x ≥ −6arrow_forward
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