. Use the second-derivative test for local extrema (: extrema for the function. Identify whether the point represents a local maximum or a local , theorem 2) to find the local 1 minimum. f(x, y) = 15x? – y? – 10y %3D

Q: 10. Find the equation of the tangent plane at (1. 1. 2) for the function f(x,y) = /6 – x² - y'· %3D

A: Here given function as fx, y=6-x2-y2 or  z=6-x2-y2 .....1

Q: A Bifolium is the family of curves given by (x +y)* = kx²y, where k is a real number constant. %3D…

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Q: y = -V16 – x², — х2, -4 < x < 0.

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Q: In which of the following is y a function of x? I. y = 9- x2 II. Jy| = x III. y = Vx² %3D O A. I…

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Q: Q1. Integrate the following functions with respect to x: y = 3x2 (1+x³)*

A: Explanation of the answer is as follows

Q: can someone please answer this right? I really need the correct answer and show all the work,…

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Q: On what interval(s) is the curve = S ₁ P y = t² t² - 5t+7 dt

A: y=∫0xt2t2−5t+7dtLeibnitz Integral Ruleddx∫g(x)h(x)f(t)dt=f(h(x))h′(x)−f(g(x))g′(x)

Q: Find the absolute extrema of the function on the closed interval. y = x ln(x + 4), [0, 3]

A: Given function: y=x lnx+4,0,3 First we shall diffrentiate the function to determine the critical…

Q: Over what interval is y undergoing positive change?   –1.15 &lt; x &lt; +1.15…

A: Step 1:For a function to undergo positive change it should move up as x increases or a tangent drawn…

Q: Y Differentiate the function below with respect to x. y = x² In (7x)

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Q: A differentiable function f is given by the table. Estimate f'(4.3): X f(x) 3.7 4.3 4.9 5.5 6.1 1.8…

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Q: Estimate f(5.03) for f as in the figure. y=f(x) (10, 4) Tangent line (4, 2) (Give your answer to…

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Q: Q4. Find the equation of the tangent plane to the function below at the speficied point z = 2x² + y²…

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