4 .. . 10) For the function f(x) = (x – 1) (x +3): a) Find the intervals of increase/decrease and local extrema. b) Find the intervals of concavity and inflection points, given that f"(x) = 12(x – 1)(x + 1). %3|

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Q: d) Find the value of the constants ´ a ' and “ b ` that makes the function continuous at x=3 ; x3

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Q: Q3: Test the following function for minimum, maximum and saddle point. f(x, y) = 4x2 -6xy+5y2- 20 x…

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Q: 8. Find the extremum and saddle points of the function f(r, y) =r' - 3ry + y if any.

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Q: Show your step-by-step solution. Find all the relative extrema and saddle points, if any, of the…

A: To find out the relative extrema and saddle points.

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Q: 1. Come up with the equation of any function f (x, y) satisfying fx = x + y and fy = x + 3y³

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Q: Find the absolute extrema of the function on the closed interval.

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Q: What is the relative extrema and saddle points of the following function? z = x² + xy + 2x + 3y 2

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Q: 3. If y = 2 x –-1, find the length of the graph of f from point z = 0 to z = 1.

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Q: 6. find all local extremum value in this function f(x)= xʻe* م م م م و و ه و و و و و و ه و و و و و و…

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Q: 8. Find the extremum and saddle points of the function f(x, y) = x³ – 3ry + y³ if any

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A: Given query is to find the minimum value of the function for the given interval.

Q: For the given function f(x, y) = y2 + xy −(1/6)x3 + 3x, find all of its relative extrema and saddle…

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Q: Q2.Find all the local maxima, local minima and saddle points of the function f(x, y) = In(x + y) +…

A: Using the rule of saddle point on f(x,y).

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Q: 5. Find the local extreme values of f(x, y) = x²y on the line a +y = 3.

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Q: 6. Determine the inflection points and intervals of concavity for the function y= e2*

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Q: 9. If f(5) = 13, f' is continuous, and f'(x) dx = 16, what is the value of f(6)?

A: Use property of definite integration

Q: Find the extremum and saddle points of the function f(x; y) = x^3 -3xy + y^3 if any.

A: we use second order partial derivative test to find out minimum, maximum and saddle point