whereas Problems 2 and 3 are about determining this information algebraically. A hint for Problem 1: remember that there are two "flavors" of critical points. . The graph of the derivative f'of a continuous function f is shown. Use the graph to determine the following. For each, give a very short description (i.e. a few words) indicating how you found them. a. critical points of f. ( notice f, not f ') y y = f(x), b. intervals where f is decreasing. 2 C. values of x where f has a local maximum. 6. d. values of x where f has a local minimum. -2 e. intervals where f concave down. f. values of x where f has an inflection point g. Assuming that f(0) = 0, sketch a graph of f using the axes given. (Recall that f is continuous.) +2 -1 5. 6. 10

Q: 1. Let Ā = (-1,2, 3) and B = (4, –3, 1). Find the following. c. [2Ã] – |3| e. JÃ – 2ĒJÄ a. JÃ|B –…

A:

Q: (x + 1)³sinx dx x+1)° cosx+3 (x + 1)2 sin x-6 (x + 1)cosx-6 sinx+ C | (x + 1) cos x 3 (x + 1)2 sin x…

A: Solving the problem by finding the integral by oarts method.

Q: 7. Inx dx

A: We need to evaluate definite integral.

Q: x2 sin x+2x cos x f'(x) = cos²x

A:

Q: Find the area of the triangle with vertices P(1,5, –2), Q(0,0,0) and R(3,5, 1). NOTE: Enter the…

A: To find the area of the triangle with vertices P1, 5, -2, Q0, 0, 0 and R3, 5, 1.

Q: Determine whether the series is absolutely convergent, conditionally convergent, or divergent.…

A:

Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

A:

Q: Use integration by part to obtain a formula for f x"e*dx and use it to find S x'e*dx. 3 5x

A: We have to find the integral

Q: |(x + 1)°sinx dx -(x + 1)³ cos x + 3 (x + 1)² sin x – 6 (x + 1)cosx – 6 sinx + C (x + 1)³ cos x – 3…

A:

Q: Given the surface x²y + y° z+ z?x = 38. Find the normal line and the tangent plane to the given…

A: A detailed solution is given below.

Q: I need help with "Determine whether the lines L_1 and L_2 are parallel, skew, or intersecting. If…

A:

Q: If+y = 25 and dz/dt = 5 , find dy/dt when y is positive and %3D %3D (a) z = 0 dy/dt = 0 (b) z=1…

A:

Q: Solve the initial value problem -4sin(2t – 4), s'(0) = 100, s(0) = 0. %3D %3D dr2

A:

Q: Determine whether (1+2)"}. u d Converges or diverges. n=0

A: Use the nth term test for the series divergence.

Q: What's the difference between average velocity and instantaneous velocity?

A:

Q: Find the exact area of the surface obtained by rotating the curve y=÷x², 0<x<12, about the y-axis.…

A:

Q: Find the volume of the solid generated by revolving the area bounded by the given curves about the…

A: Given problem:- Find the volume of the solid generated by revolving the area bounded by the given…

Q: Consider the function f(x) = 12x + 75x 120x + 3. f(x) has inflection points at (reading from left to…

A: The given function is: f(x)=12x5+75x4-120x3+3 Now, the derivatives of the functions are:…

Q: Solve this q3 as soon as possible and not use p. Take (p=6) and solve this plz with p=6

A: Follow the procedure given below.

Q: Write and evaluate the definite integral that represents the volume of the solid formed by revolving…

A: As we know that; The expression for the volume of the revolution of the function y=fx from x=a to…

Q: Which of the following is the inverse of the functionf : [0, ∞) → [3, 0), f(x) = 2.x² + 3? Select…

A:

Q: (csc e cot é -s cot 6 de

A:

Q: Use seperation of variable to solve the following differential equation (DE): (11 + x) dy – y dx = 0…

A:

Q: 2 : x = 1 + 3t, y = 3 – 6t, z = 5 – 3t are parallel and find the distance etween them. FOTE: Enter…

A:

Q: 4y° sin°(x) x10 + y10 if (x, y) + (0,0) Let f(x, y) if (x, y) = (0,0) sin(4æy) if (x, y) + (0,0) and…

A:

Q: SIn?C3x) +C 4

A: To find the missing value in the integral expression.

Q: Find the relative maximam/minimum values of the fuction てキX Stak where the Function S increasing of…

A: For a given function, y = F(x), if the value of y is increasing on increasing the value of x, then…

Q: Consider the function f(x) = 2x + 18x? – 42x + 9, - 7< x < 2. This function has an absolute minimum…

A:

Q: Suppose that o f (x) dx = 3. Find L f(x) dx if, %3D

A:

Q: 5) x²dx + y(x – 1)dy = 0 %3D

A:

Q: 1. Always show your solutions. 2. Write legibly and SCAN your work clearly. 3. Be sure that all…

A:

Q: pleasee answer C and E

A:

Q: x + 1 24. x*(x - 2)

A: Question no. 24,Given,            x+1x2x-2To find : Find the partial fraction decomposition of given…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A:

Q: A box with a square base and open top must have a volume of 4000 cm. Find the dimensions of the box…

A:

Q: Problem : Find the derivative of the series 2x 4x2 8x3 16x4 32x5 f(x) =1+ 1! 2! 3! 4! 5! Also show…

A:

Q: dy 1+ y+1

A:

Q: T sec"(evE + 1) dx Vxe-Vx

A:

Q: 1. * Sx² sin 2x dx -x²cos2x ¸ x sin 2x , cos 2x +C 8. –x²cos2x x sin 2x , cos 2x + C A 2 2 B…

A: To Find : ∫x2sin(2x)dx

Q: panding such that its length is always 4 times its width. If the ng at a rate of 0.5 cm/min, is its…

A:

Q: pls show full solutions and clear   1. Show that the absolute value function is continuous at x =…

A:

Q: Find the relative maximam/minimum values of the fuction f(x)=X-2 State where the function is…

A: Given,            fx=x-2x+2To find : Find the relative maximum/ minimum values of the function.…

Q: Stxª_ 3x3+ D -2)x= * (8x* -30,3+5x-80) x (8x1 -30x3+5x-80) 40

A: This question can be solved solved using integration as the inverse process of differentiation.

Q: St' sin(2t*)dt (sin(2t*) - 2t*cos (2t*)) + C (sin(2t*)-2t cos (2r*)) +C 14 1 (sin(2t*)-2t cos (2t*))…

A:

Q: let w=ln(x2+y), x= 2t, y=4-t. compute dw/dt a) using the Chain rule, draw corresponding tree diagram…

A:

Q: lim g(f(2)) = * - 00 lim g(f(2)) = |0 lim *-1+ g(f(2)) = 00 lim g(f(x)) -00 *-2-

A:

Q: Determine whether the improper integral (3- is convergent or divergent.

A: The given integral,       ∫1∞3-2x-32dx

Q: Is the line through (4, 1, – 1) and (2, 5, 3) perpendicular to the line through (-3, 2, 0) and (5,…

A:

Q: Evaluate the following limit: lim (7,y)→(0,0) 5æ6 + 6 sin°(y) 14x6 + y6 3 4 11 15 2 3 The limit does…

A:

Q: * | 2x)cx csch (2 sin -1 V1-4x²

A: The given integral,       ∫csch2sin-12xdx1-4x2