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Answer both questions please Question 13 0/ 1 point If we are given a graph which...
Answer both questions please
Question 13 0/ 1 point If we are given a graph which shows a plot of the position as a function of time, xt), how will the instantaneous yelocity at point C be related to the graph? A) it would equal the slope of the line tangent to the x(t) curve at point B B) it would equal the slope of the line tangent to the x(t) curve at point C C) it would equal the...
2. (Section 4.2) Given f(x)-x on the interval [0,4], complete the following (a) Verify that the f...
2. (Section 4.2) Given f(x)-x on the interval [0,4], complete the following (a) Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval. b) Find the number c that satisfies the conclusion of the meat value theorem on the given interval. (c) Sketch a neat, clearly labeled graph with the function, the secant line that goes through the end points, and the tangent line at (c./(c)) all on the same coordinate grid (d) Are...
A. Determine whether the Mean Value Theorem applies to the function fx)xon the interval [3,7 b. I...
a. Determine whether the Mean Value Theorem applies to the function fx)xon the interval [3,7 b. If so, find or approximate the point(s) that are guaranteed to exist by the Mean Value Theorem. c. Make a sketch of the function and the line that passes through (a,f(a) and (b.f(b). Mark the points P (if they exist) at which the slope of the function equali of the secant line. Then sketch the tangent line at P A. No, because the tunction...
Graph of A continuous function fis defined on the closed interval - 4sxs6. The graph of...
Graph of A continuous function fis defined on the closed interval - 4sxs6. The graph of consists of a line segment and a curve that is tangent to the x-axis at x-3, as shown in the figure above. On th interval Dexc6, the function fis twice differentiable, with f(x)>0. Is there a value of a -4sach, for which the Mean Value Theorem applied to the interval (a 6), guarantees a value ca cx6, at which f'(c) = ? Justify your...
*5. A function f defined on an interval I = {x: a <x<b> is called increasing...
*5. A function f defined on an interval I = {x: a <x<b> is called increasing f(x) > f(x2) whenever xi > X2 where x1, x2 €1. Suppose that has the inter- mediate-value property: that is, for each number c between f(a) and f(b) there is an x, el such that f(x) = c. Show that a functionſ which is increasing and has the intermediate-value property must be continuous. This is from my real analysis textbook, We are establishing the...
3c and 3d 3. Given the function defined by fx)-2x3x-12x+ 20. a) By using Rational Root...
3c and 3d
3. Given the function defined by fx)-2x3x-12x+ 20. a) By using Rational Root Theorem and Synthetic Division, write flk) as a product of its factors dentily the zeros. b) The slope function can be found by using the formula: (lnxWrite the equation of the line tangent to the graph offat x 0. c) A tangent line drawn to the graph of f is said to be a horizontal tangent or parallel to x-axis if the slope is...
c. 2 d. 3 3 5. Find the absolute maximum of the function Ax)-xx+ 1)0x-1) on...
c. 2 d. 3 3 5. Find the absolute maximum of the function Ax)-xx+ 1)0x-1) on the interval 0sx2. b. 0 d. 8 Find the slope of the tangent to the graph of -x(x2-*) at its point of infection. 6. a. 0 b. 2 c. 4
x²+2x+2 4. Let y=f(x)= x² – 3x-5 (a) Find f(3) (b) Find and simplify f(x) -...
x²+2x+2 4. Let y=f(x)= x² – 3x-5 (a) Find f(3) (b) Find and simplify f(x) - $(3) X-3 f(x)- $(3) (c) Find lim X-3 (d) Find and simplify $(3+h)-f(3) h 13 (e) Find lim f(3+h) – S (3) h 0 h (t) Find the slope-intercept form of the tangent line to y = f(x) at x = 3. (g) Plot the curve and the tangent line on the same graph, using the form on the window (-3,7]*[-10,10). 5. A car...
Math 32-_ Multivariable Calculus HW 3 (1) Consider the two straight lines L1 : (2-t, 3...
Math 32-_ Multivariable Calculus HW 3 (1) Consider the two straight lines L1 : (2-t, 3 + 2t,-t) and L2 : <t,-2 + t, 7-20 a) Verify that L1 and L2 intersect, and find their point of intersection. (b) Find the equation of the plane containing L1 and L2 (2) Consider the set of all points (a, y, z) satisfying the equation 2-y2+220. Find their intersection 0 and 2-0. Use that information to sketch a with the planes y =-3,-2,-1,0,...
Question 19 3 pts 5 1 0 Details Find all the values of x where the...
Question 19 3 pts 5 1 0 Details Find all the values of x where the graph of f(a) 2x3 – 30x2 + 542 – 6 has a horizontal tangent line. The smaller one is x = and the larger one is x = Question 20 3 pts 5 1 0 Details Consider the function f(x) = 3x2 – 8x + 1, 0 < x < 8. The absolute maximum of f(x) (on the given interval) is at X =...
Answer both questions please
Question 13 0/ 1 point If we are given a graph which shows a plot of the position as a function of time, xt), how will the instantaneous yelocity at point C be related to the graph? A) it would equal the slope of the line tangent to the x(t) curve at point B B) it would equal the slope of the line tangent to the x(t) curve at point C C) it would equal the...
2. (Section 4.2) Given f(x)-x on the interval [0,4], complete the following (a) Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval. b) Find the number c that satisfies the conclusion of the meat value theorem on the given interval. (c) Sketch a neat, clearly labeled graph with the function, the secant line that goes through the end points, and the tangent line at (c./(c)) all on the same coordinate grid (d) Are...
a. Determine whether the Mean Value Theorem applies to the function fx)xon the interval [3,7 b. If so, find or approximate the point(s) that are guaranteed to exist by the Mean Value Theorem. c. Make a sketch of the function and the line that passes through (a,f(a) and (b.f(b). Mark the points P (if they exist) at which the slope of the function equali of the secant line. Then sketch the tangent line at P A. No, because the tunction...
Graph of A continuous function fis defined on the closed interval - 4sxs6. The graph of consists of a line segment and a curve that is tangent to the x-axis at x-3, as shown in the figure above. On th interval Dexc6, the function fis twice differentiable, with f(x)>0. Is there a value of a -4sach, for which the Mean Value Theorem applied to the interval (a 6), guarantees a value ca cx6, at which f'(c) = ? Justify your...
*5. A function f defined on an interval I = {x: a <x<b> is called increasing f(x) > f(x2) whenever xi > X2 where x1, x2 €1. Suppose that has the inter- mediate-value property: that is, for each number c between f(a) and f(b) there is an x, el such that f(x) = c. Show that a functionſ which is increasing and has the intermediate-value property must be continuous. This is from my real analysis textbook, We are establishing the...
3c and 3d
3. Given the function defined by fx)-2x3x-12x+ 20. a) By using Rational Root Theorem and Synthetic Division, write flk) as a product of its factors dentily the zeros. b) The slope function can be found by using the formula: (lnxWrite the equation of the line tangent to the graph offat x 0. c) A tangent line drawn to the graph of f is said to be a horizontal tangent or parallel to x-axis if the slope is...
c. 2 d. 3 3 5. Find the absolute maximum of the function Ax)-xx+ 1)0x-1) on the interval 0sx2. b. 0 d. 8 Find the slope of the tangent to the graph of -x(x2-*) at its point of infection. 6. a. 0 b. 2 c. 4
x²+2x+2 4. Let y=f(x)= x² – 3x-5 (a) Find f(3) (b) Find and simplify f(x) - $(3) X-3 f(x)- $(3) (c) Find lim X-3 (d) Find and simplify $(3+h)-f(3) h 13 (e) Find lim f(3+h) – S (3) h 0 h (t) Find the slope-intercept form of the tangent line to y = f(x) at x = 3. (g) Plot the curve and the tangent line on the same graph, using the form on the window (-3,7]*[-10,10). 5. A car...
Math 32-_ Multivariable Calculus HW 3 (1) Consider the two straight lines L1 : (2-t, 3 + 2t,-t) and L2 : <t,-2 + t, 7-20 a) Verify that L1 and L2 intersect, and find their point of intersection. (b) Find the equation of the plane containing L1 and L2 (2) Consider the set of all points (a, y, z) satisfying the equation 2-y2+220. Find their intersection 0 and 2-0. Use that information to sketch a with the planes y =-3,-2,-1,0,...
Question 19 3 pts 5 1 0 Details Find all the values of x where the graph of f(a) 2x3 – 30x2 + 542 – 6 has a horizontal tangent line. The smaller one is x = and the larger one is x = Question 20 3 pts 5 1 0 Details Consider the function f(x) = 3x2 – 8x + 1, 0 < x < 8. The absolute maximum of f(x) (on the given interval) is at X =...
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