Derivatives Trigonometric Functions IB Math MCV4U TEST

Q1. Determine the derivatives of each of the following functions.
a. f(x)=sin^4⁡x
b. f(x)=x^3 sin⁡x-1/2 cos⁡2x
3. f(x)=tan⁡(5-sin⁡2x )
Q2. Determine the derivatives of f(x)=(sin⁡x/(1+cos⁡x ))^2.
Q3. Find the equation of the tangent line, in y = mx + b, at x=5π/4
Q4. Determine the x-coordinate(s) at which the graph of the given function has a horizontal tangent line. f(x)=x+2 sin⁡〖x,from [0,2π]〗.
Q5. The displacement from equilibrium of an object in harmonic motion on the end of a spring is s(t)=1/3 cos⁡12t-1/4 sin⁡12t, where y is measured in meters and t is time in seconds. Determine the velocity at t=π/8 s.
Q6. Determinethe absolute maximum and minimum points for the given interval.
f(x)=sin^2⁡x+sin⁡x, [0,3π/2]
Q7. If y=sin⁡(2x+3), show that y"+4y=0
Q8. Let f(x)=sin⁡x+1/2 x^2-2x,for 0≤x≤π and g(x)=1/2 (x-2)^2+3. Find the value of x for which the tangent to the graph of f(x) is parallel to the graph of g(x).
Q9. The graph of f(x)=a sin⁡〖[b(x-c)]+d,2≤x≤10〗 has maximum at P(4, 12) and minimum at Q(8, -4).
a. If the point A(2, 4) lies on the graph find the value of a, b, c, and d.
b. At the point B, the slope of the tangent line if -2. Find the x-coordinate of B.
Q10. Given y=1/4 tan⁡x+1/x^2 ,[0,π] solve the equation dy/dx=1-2/x^3 . #GCSE #SAT #EQAO #IBSLmath

[parasar]

good to see you sir...
in which school do you teach?

[bttrv]

I believe you missed negative sign in solution at 3.59.

[aqmalfiqri]

In Q4, at 12th minutes, I think you accidentally wrote 0 = 2 - cos x when it's suppose to be 0 = 2 + cos x.