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...

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...

Could someone help me check if I differentiated these these two functions correctly: f(x)= √(3x2-x3) And h(x) = 3√(5x+x2)2 I...

f(x) = x3 - 8x2 + 5x Compute algebraically the x-coordinates of the points on the graph of f where the tangent to this graph is horizontal. I know...

x2y2 +y+1=0

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...

Differentiate the following function and simplify. h(x) = x2 · √8-x Answer = 2x√8-x - x/2√8-x Could you show me the step by step process...

y= -x5(1 - x) I have to use the product rule to answer this question. The answer is 6x5 - 5x4 Can someone explain this to me and show how to...

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...

In order to construct a box whose base length is 3 times the base width with volume of 50 ft^3, using materials to build the top and bottom that cost $ 10 per ft^2 and $ 6 per ft^2 for the sides....

Cos(logx + ex)

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...

The angular acceleration of a system is described by the following equation: a(t)=d^2Radians/dt^2=10cos (5t). Find the angular velocity of the system in radians after 14 seconds

I need help with part C as i am unsure what value i should put into x to find the +C part a + b + c: a) show that there is a single value of x for which the curve has...

Hi I have been given a function f:(a,b)→R, which is differentiable on (a,b). How do I use this information to prove that f is also continuous on (a,b)? Thanks.

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...

Calculus, Differentiation

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

g(x) = x2(1 − 8x)

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