(b) Given that 1.0 1.3 1.4 1.5 1.1 1.2 1.6 y = f(x)7.989 8.403 8.781 9.1299.4519.750 10.031 dy Find and de at a = 1.1 and a = 1.6. Recall that: dy da A yo – Yo Yo d'y ☆[△ yo-△° yo + 끓 △ yo-응 △ yo + 137 A yo- 180 da Vyn + V²yn + £v°yn + }V*yn+. ..] da d²y da? V?yn + V°yn + V*yn + { V°yn + 180 V°yn+… . ] 137

Q: dy 23. If y=f(x² - 2x + 7) and ƒ (10) = 2, determine at x = 3. Show your work. 2T dx a. 2 b. 6 C. 8…

A: Given:         y=fx2-2x+7   and  f'10=2 Then dydx at x=3 is:      y=fx2-2x+7 differentiating with…

Q: 15. Which of the following is a point at which the tangent to y = (x − 2)²(x + 3) is horizontal?…

A:

Q: Consider the following table of data associated with the function i Xi 0 1.0 f(x)=ln(x). Use…

A: We need to approximate the value of f(3.2) using the first and second order Newton's polynomials for…

Q: 5. The graph of f is shown below. Use the indicated areas (physical areas), in units?, of the…

A:

Q: If f(-0.1) = 5, f(O) = 7, and f(0.1) = 8 then f'(0) is approximately equal to: a. 0 Ob. 15 Ос. 30…

A:

Q: +larctan(4))

A:

Q: 2. Sketch a stencil over which the following data (and an appropriately derived formula) could be…

A: As per the question we are given the following data : x 0.5 1.0 1.5 2.0 f(x) 0.095 0.191…

Q: 2, f'(4)=2, f'(4)= -1 se correct graph below. OB. Oc. OD. Ay Ay Ay (4, 2) (4,2 (4,2) (4, 2)

A: Solve by using first derivative and second derivative

Q: 3. 6. Given the representativec Set its table of variations in e up 1° yA 2) x' -2-1 01 2 3 4

A: according to our terms and condition i have solved question 1 and for next question repost

Q: 9. Below is the graph of a function along with its tangent and normal at the point (1,8). Find the…

A: a.Abscissa is the x-coordinate of the the given point (1,8), therefore x = 1. b. Ordinate is the…

Q: . Determine the equation of the tangent line to the function f(x) = e* sin sin x at x x = ²/1/2

A:

Q: Here R^3 - {(0,0,0)}. please proof this using submersion. thank you.

A: Given: R3=(0,0,0) To find: The set M=(x,y,z)∈R3:x2+2y2+z2=4xyz a submanifold of R3.

Q: 9. Below is the graph of a function along with its tangent and normal at the point (1,8). Find the…

A: Step 1: Find the abscissa and ordinate.In common usage, the abscissa refers to the x coordinate and…

Q: 1.3 The distance D, in meters that an object has fallen after t seconds is given by D(t) = 16t². i.…

A: Slope = (Y2-Y1)/(X2-X1)

Q: If fe F dr = Sc(x - 2y³) dx + (x²y) dy, what is F?

A:

Q: 13. z = Vy – x, (1, 2, 1) %3D

A:

Q: The graphs of f and g are shown below. If h(x)= f (x)g(x), then h'(6) = а. -9 b. -7 с. 1 d. 7 | | |…

A: First we difine the function help of given graph. And  we derivative of h(x) then we get h'(x) and…

Q: | s(x) dx is positive, negative, or zero. [4.3] Decide whether 26. УА 27. УА b x

A:

Q: se the graph of the function below to establish the sign of its second derivative

A:

Q: X Y Find Y' (5) from the following table? 0.0 1 2 3 0.0 2.5 8.5 15.5 a) Y = 13.13 b) Y = 13.5 c) Y =…

A:

Q: 7. What is the amplitude of the following function? а. 1 b. 1.5 c. 1.75 d. 2 e. 4 .0:5-

A:

Q: If f(x.y)=sin (2x+y) then the derivative f, Is 2 cos (2x+y) a. b. cos (2x+y) c. 2 sin (2x+y) d. 2…

A:

Q: S x dx/(x² - 3) = In]x? - 3| + c * %3D O False O true If y= csch3x then dy/dx = - 3 csch3x %3D…

A:

Q: 3Q. Using Forward, Backward and Central differences find the first order derivative at x=1.1 from…

A:

Q: 5. For ø = z sech¯³[y tan¬²(In x)], find the directional derivative when dx = 2dy = –3dz at a point…

A: Given function is ϕ=zsech-1ytan-1lnx we have to find the direction derivative of given function when…

Q: Rocky Mountain Chocolate Factory (RMCF) founder and president Frank Crail employs 220 people in 361…

A: for net price  equivalent rate determine first find the complement of the chain discount rate…

Q: IV. Obtain the 2nd Derivative of the given function. 7. 4y – xy? 1

A:

Q: A y y 4 -5 15 1 1 12.5 1 8 10 2. 16 10 3 7.5 3 32

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Suppose we have a function f such that f(5) = 32 and f(5) =-2. Estimate the following values (round…

A: Given that: f(5)=32f'(5)=-2

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.