5. (cont.) Using f(x) = x ln √√x + 2x ; Do each of the following: C. Perform the 1st derivative test for relative extrema. d. Perform a test of concavity.

Q: Find the derivative of y with respect to x if y = (11x2 - 22x+ 22) ex.

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Q: 16. / cot(z) dr 17. cot (x) dr 18. csc(r) dr

A: (16) ∫cot(x)dx ∫cot(x)dx=∫cosxsinxdxPut t=sinx      dt=cosxdx we get-∫cot(x)dx=∫1tdt…

Q: 2. (a) Define what it means by for y = f(x). %3D

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Q: 2 6. For the function(x) = 2x² approximate the slope of the tangent line at (1,2)

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Q: 4. Find the equation of the tangent to f (x) = 4x² + 12x, at x = -3. Use first principles.

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Q: If f(x) = (x+4)sin(√x+4), what is the average off on the closed interval [0, 5]? Round to 3 decimal…

A: Step 1:  Step 2: Step 3: Step 4:

Q: : For u = -2xy + x, check the function for Harmonic and then find f(z).

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Q: 4. Given f(x) = sin² (2x) find the slope at (5, 1) a)-√3 b) √3 d) 0.1395

A: As we know that; The slope of the tangent line to the given curve is equal to the derivative of the…

Q: Let p(x) = x³ + 3x? – 9x + 10. Find two values of æ for which the tangent line through the point (x,…

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Q: The derivative of the functionf (x) which is given by f (x) = x - 2x+ 3 at x = 4 is D. 10 E. 4 A. 59…

A: To find the derivative of a function at x= 4 we will differentiate the function w.r.t. x and then…