Find the second derivative of the function.
y = 4(x2 + 2x)3
y" = _______
Find the third derivative of the function.
f(x) = x4-4x3
f'''(x) = _______
Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an answer does not exist, enter DNE.) f(x) = x4 - 4x3 + 1 relative maximum (x,y) - relative minimum (x, y)
Let f(x)=(x? + 1)^(2x – 1) is a polynomial function of fifth degree. Its second derivative is f"(x) = 4(x2 + 1)(2x – 1)+8x²(2x – 1)+ 16x(x? + 1) and third derivative is f"(x) = 24x(2x – 1) +24(x + 1) +48x2. True False dy Given the equation x3 + 3 xy + y2 = 4. We find dx 2 x' + y by implicit differentiation and is to be y' = x + y2 True False Let f(x)= x...
Using the definition, calculate the derivative of the function. Then find the values of the derivative as specified. f(x) = 3 + x2: f'(- 9), F 'O), f (9) Using the definition, calculate the derivative of the function. Then find the values of the derivative as specified. 4 96) = 3. g'(-2), g'(4), g(6) o't)= dx if y = 7x3 dy || s={3 - 4+, t= -6 s'(t)= 0 ne indig y=f(x)= 3 + 14-x, (x,y)= (0,5) The derivative of...
Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an answer does not exist, enter DNE.) f(x) = x2 + 3x – 9relative maximum (x, y) = _______ relative minimum (x, y) = _______ Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an answer does not exist, enter DNE.) f(x) = x4 + 16x3 - 7 relative maximum (x, y) = _______ relative minimum (x, y) = _______
34 & 38 please 33-42 Use logarithmic differentiation to find the derivative of the function. 33. y = (2x + 1)*(x4 – 3) 35. y = sin’x tanºx (x² + 1) 36. y = 34. y = (x e*'(x² + 1) 10 x2 + 1 r2 - 1 38. y = rcos 40. y= Vit 42. y = (sin x) In x 37. y = x 39. y = (cos x)* 41. y = (tan x) /
5. Create a MATLAB script to find the first and second derivative of given function using Forward, Backward, central and Taylor numerical schemes. Test your code using the following functions: f(x)-xe*+3x2 +2x -1 and find f (3) and f' (3) for with h 0.1, 0.01 and 0.001 b. Approximate y'(1) and y"(1) using the following table f(x) 0.992 0.8 0.9 0.999 1.0 1.001 1.008 Input: (copy and paste the MATLAB or Scilab script in the following box) 5. Create a...
Find the derivative of the function. F(x) = (x4 + 3x2 - 2) F'(x) F(x) = Find the derivative of the function. f(x) = (3 + x)2/ f'(x) = Find the derivative of the function. g(t) = 7+4 + 4)5 g'(t) =
Find the critical points of the following functions. Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, local minimum, or saddle point. f(x, y) = e-X2-y2-2x
QueBLIUI JI JPLS Find the requested value of the second derivative of the function. f(x) = 7x2 + 9x - 3; Find f"(0). 14 00 -14 Question 32 5 pts Find the indicated absolute extren um as well as all values of x where it occurs on the specified domain f(x) = * x3 - 2x² + 3x - 4; (-2, 5] Minimum 0 -4 at x = 0 at x = -2 atx = 2 Question 33 5 pts...
Find the derivative of the function. g(x) = 800(3 - e-0.1x) Find the derivative of the function. y = :ets Find the derivative of the function. y = 4e(x2 + 6)3 Find the derivative of the function. y = In(e2x + 3)