5. Find the e-coordinate of the point on the curve : +3y3 = 3ay where the...
How many real roots does the equation æ4 – 9x2 + c = 0 have in the interval (-3,0]? Hint: use the Mean Value Theorem (Rolle's Theorem). Show your work in the PDF version of the test.
Find the x-coordinate of the point on the curve 23 + 3y3 = 3xy where the tangent is horizontal. Show your work in the PDF version of the test.
Two sides of a triangle are 8 m and 9 m in length and the angle between them is increasing at a rate of 0.05 rad/s. Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is 7/3. Show your work in the PDF version of the test.
Two sides of a triangle are 8 m and 9 m in length and the angle between them is increasing at a rate of 0.05 rad/s. Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is 7/3. Show your work in the PDF version of the test.
9. Find the absolute maximum value of the function (1) = 2/32 - sin(4x) on the interval (0, 8/12). Show your work in the PDF version of the test.
) 8. Suppose a triangle is constructed where two sides have fixed length a and b, but the third side has variable length x You can imagine there is a pivot point where the sides of fixed length a and b meet, forming an angle of θ. By changing the angle θ, the opposite side will either stretch or contract (a) Let K(x)- Vs(s - a)(s -b)(s - x), where s is the semiperimeter of the triangle. Accord ing to...
Find the absolute maximum value of the function f(x) = 2V3x – sin (4x) on the interval [0, 7/12]. Show your work in the PDF version of the test.
Find the absolute maximum value of the function f(x) = 2V3x – sin (4x) on the interval [0, 7/12]. Show your work in the PDF version of the test.
5. (4pts, each) In each part, list the point (A-E) on the graph off whose x-coordinate satisfies the given conditions. (a) f'(x) > 0. and F"(x) > 0 (b) f'(x) <0. and f"(x) = 0 (c) f'(x) = 0.and f"(x) < 0 6. (12pts) Find all critical numbers of f(x) = x + Then use the second-derivative test on each critical number to determine whether it leads to a local maximum or minimum. Show your work to get a full...
use matlab and show all codes and work the question continues from this 4. Write a function with header (A, V - myCone (r, h), which outputs the total area A and volume of a cone with base radius r and height h. 5. Write a function - myMatrix (myvec, m, n) which creates an m-by-n matrix A, as in Problem 3, but for arbitrary values of mand n and any length of vector myvec. Hint: the function can use...