Tutorial Exercise Consider the following problem. Find the distance traveled in 29 seconds by an object traveling at a constant velocity of 21 feet per second. Decide whether the problem can be solved using precalculus, or whether calculus is required. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.
Consider the following problem. A bicyclist is riding on a path modeled by the function f(x) = 0.04(8x − x2), where x and f(x) are measured in miles. Find the rate of change of elevation when x = 2. (Round your answer to two decimal places. ) Decide whether the problem can be solved using precalculus, or whether calculus is required. The problem can be solved using precalculus. The problem requires calculus to be solved. If the problem can be solved using precalculus, solve it. If the problem seems to require calculus, use a graphical or numerical approach to estimate the solution.
Consider the function f(x) = 4x − x2 and the point P(2, 4) on the graph of f. Part (a) Graph f and the secant lines passing through P(2, 4) and Q(x, f(x)) for x-values of 3, 2.5, 1.5. Part (b) Find the slope of each secant line. Part (c) Use the results of part (b) to estimate the slope of the tangent line to the graph of f at P(2, 4). Describe how to improve your approximation of the slope.
Consider the figures below. (1) (2) (a) Use the rectangles in each graph to approximate the area of the region bounded by y = 5/x, y = 0, x = 1, and x = 5. (Round your answers to three decimal places.) figure (1) figure (2) (b) Describe how you could continue this process to obtain a more accurate approximation of the area. Continually decrease the number of rectangles. Continually increase the number of rectangles. Continually decrease the height of all rectangles. Continually increase the height of all rectangles.
Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE. ) y = x2 x2+27 intercept (x, y) = ( ) relative minimum (x, y) = ( ) relative maximum (x, y) = ( ) points of inflection (x, y) = ( ) (smaller x-value) (x, y) = ( ) (larger x-value) Find the equation of the asymptote. Use a graphing utility to verify your results.
Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE. ) y = x2+3 x2−64 intercept (x, y) = ( ) relative minimum (x, y) = ( ) relative maximum (x, y) = ( ) point of inflection (x, y) = ( ) Find the equations of the asymptotes. (smaller x-value) (larger x-value) (horizontal asymptote) Use a graphing utility to verify your results.
Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE. ) f(x) = x2−11x+54 x−9 intercept (x, y) = ( ) relative minimum (x, y) = ( ) relative maximum (x, y) = ( ) point of inflection (x, y) = ( ) Find the equations of the asymptotes. (vertical asymptote) (slant asymptote)
Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of inflection, and asymptotes. (Order your answers from smallest to largest x, then from smallest to largest y. If an answer does not exist, enter DNE. ) y = 12(x−1)2/3 − 4(x−1)2
Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of inflection, and asymptotes. (If an answer does not exist, enter DNE. ) y = 5−4x−x3 intercepts (x, y) = ( ) (smaller x-value) (x, y) = ( ) (larger x-value) relative minimum (x, y) = ( ) relative maximum (x, y) point of inflection (x, y) = ( ) Find the equation of the asymptote. Use a graphing utility to verify your results.