f(x) = √(x^2-10x+10)     f′(x) = 2x-10 / 2√(x^2-10x+10)     What are the local extremes and what are their coordinates?   Is it a maximum...

A cone-shaped container with a hole at its top vertex is filled with water. The cone has a 4cm radius and 16cm in height. The cone was turned upside down to the let its water flow out of container...

b) For the curve 𝑦=𝑥𝑒^−𝑥^2 ,𝑥 ≥0 i. Find the coordinates of the point where the gradient is 0 giving your answers exactly. ii. Show that the line 𝑦=𝑥 is a...

Need help with a question on differentiation.   *Determine the exact coordinates of the local extreme(s) of the following function. Also indicate whether it concerns a local minimum or...

A system in a lab is tested under two different conditions. The angular acceleration of the system s described by the equations: a(t)=d^2const/dt^2=10cos (5t). Find the angular velocity of the...

A farmer wants to fence his farm with a fencing material of total length 300 m such that fenced area is minimum. He fences it such that he obtains a square and a rectangle sharing a common...

show that :f'(x) = 1/ xsinx (sec^3 x + (1-1/x)secxtanx)

show that: f'(x) = 1/xsinx (sec^3 x + ( 1 - 1/x) sec x tan x )