Therefore, we can modify #1 + x + x^2 + x^3 + ...# to get the power series for the first half, # (x)/ (1-x)^2#, by taking the derivative of every term and multiplying every term by #x#.

This means that is may be a point of inflection. We can check a graph of the function: graph {-5x^5-2x^4-2x^3+14x-17 [-2.5, 2.5, -120, 100]} Graphically, x=0 does appear to be a point of …

Explanation: The concavity of a function can be determined through the second derivative; a positive value indicates it is concave at that point (curving upward), and a negative value …

I need to know second order derivative d2y dx2 for 6xy6 − 2y 1 2 = 52y2 using implicit differentiation at point (9, 1)? I can get the first order differentiation just fine.

How do you find and classify all the critical points and then use the second derivative to check your results given #y=x^2+10x-11#? How do you find the slope and equation of the tangent …

Write F as (x-a) times G (x) where G is all the factors of F except the first one. F (x) = (x −a)G(x) its derivative is (using the product rule) F' (x) = (x-a) G' (x) + (x-a)'G (x) so far so good. Now for …

A = 25 Given: y = -4x+20 The area of the rectangle is: A = xy Substitute y = -4x+20: A = x (-4x+20) A = -4x^2+20x (dA)/dx = -8x+20 (d^2A)/dx^2 = -8 Because the second derivative is …

A necessary condition for the function to have an inflection point is that the second derivative vanishes. Calculate the second derivative: f (x) = x + 4 (x − 2)2 f ...

Aug 16, 2017 · See explanation. Questions 22 and 24 are the basic properties of derivatives. 22 says that the derivative of a difference of 2 functions is the difference of the functions' …

A person travels the total distance in two parts in ratio 2:1 with a constant speed of 30km/h in the first part and 40km/h in the second part.What is average speed of the journey? If #f= { (-3,4), ( …