8.3 (a) Use the first derivative test and the second derivative test to justify the saddle points and the local extrema points of z = x - y³ - 2x² + 3y + 1. (b) Calculate the local maximum values and and local minimum values using the function formula.

Q: Find all local maximum and minimum points of y = 2 + 3x − x³ by the second derivative test.

A: y = 2 + 3x - x3    => y' = dy/dx = 3 - 3x2 = 0 (set)                => 3(1 - x2) = 0…

Q: a) Determine the first derivative. f(x)= x³ - 5x² + 3x + 2 b) Determine critical points, and…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Given S(x) = x* –12x². i) Find if exist, the maximum and minimum points of the curve by using second…

A: We will use the second derivative test to find the maximum and minimum points of the curve.

Q: My topic is about Higher Order Derivatives and Optimization for reference. A cardboard box…

A:

Q: Let f(x)=x+(1−x)^(1/2) Find the local maximum and minimum values of f using both the first and…

A: For local maxima or minima:The first derivative test is f'(x) = 0The second derivative test…

Q: 3. Find the points (x,y) of the function f(x) = -x³ + 12x² - 5 where the tangent is horizontal AND…

A:

Q: 1. Find the derivative function for the following using the power rule: a) f(x) = x¹² b) y = 8x³ -…

A: Since the student has posted many sub-parts of the question and does not mention any specific part,…

Q: Use the derivative to determine the local minima and maxima. If a minimum and maximum does not exist…

A:

Q: a) y = −8x² + 4x¯¹ − 2 b) f(x)=√√x - √x 5 c) g(x) = x³

A:

Q: in his model for storage and shipping costs for a manufacturing process, a researcher develops the…

A: Step 1: First, simplify the equation of the storage.Step 2: Then, differentiate the equation with…

Q: Let f (x) = a +x² 3x - Ca) Determine the y intercept of f(x) and any symmetry. (Don't ind the…

A: Given: Graph of function:

Q: f(x) = (4x² + 3x)² h(x) = 7 (4x³ - 6x²)³ b) d) g(x)=√10x² - 5x y = 1 3/(x ³√(x + + 5)²

A: We have to find out derivative for different functions.

Q: Q1 Prove that the derivative of (2x +1)2 is 4 (2x + 1) by using first principle derivative.

A: as per our guidelines we are supposed to answer only the first question. Kindly repost other…

Q: a) y = -5x6 b) y = 6x2 c) f(x) = -7

A:

Q: (B) Use the first derivative test to find the maxima and minima for f(x) = 3. 5z2 + 6x +9. 2.

A:

Q: b) f(x)=√x - √x c)

A:

Q: Find an equation of the tangent line to y = f(x) at x = -2. (Using the definition) f(x)=x² + x² + x…

A: we have, Differentiating w.r.t x, we getDifferentiating again w.r.t x, we getFurther,    .     .…