1,2.3 Given that y-2x-3x2 - 12x, (a) find coordinates of all the critical points, (b) classify(max...

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1,2.3 Given that y-2x³-3x2 - 12x, (a) find coordinates of all the critical points, (b) classify(max or min) these points using 2nd derivative test, (c) find the intervals in which y is decreasing, (d) find the global maximum and minimum of y, -2≤ x ≤ 3, (e) find the abscissa of inflection point if any (e) sketch the graph clearly indicating local max and min. 4 A rectangular container with four sides, open top and square bottom is to have 2000 cubic units What are the dimensions of the container with the minimum surface area? 5. Find (a) y=x³sin( 5x²-3x), (b) y=√¹ Find the slope and equation of the line tangent to the curve y= 2√x - 8x at x-2 (a) Volume of a cube is increasing at the rate of 20 ft³/min. How fast is the side of the cube increasing when the side is 3 ft ? (b) Find: 4x2y4-4y+5x³-3=0. 6. 7. 8. (a) Using differential find approximate value of √79. (b) If the possible error of the measurment of the radius of a sphere is 20 cm .find approximate error in the measurement of the volume. 9 (a) Solve DE y = 4√x-6x,y(4) = 2 (b) (4√x - 6x) dx. 1,2.3 Given that y-2x³-3x2 - 12x, (a) find coordinates of all the critical points, (b) classify(max or min) these points using 2nd derivative test, (c) find the intervals in which y is decreasing, (d) find the global maximum and minimum of y, -2≤ x ≤ 3, (e) find the abscissa of inflection point if any (e) sketch the graph clearly indicating local max and min. 4 A rectangular container with four sides, open top and square bottom is to have 2000 cubic units What are the dimensions of the container with the minimum surface area? 5. Find (a) y=x³sin( 5x²-3x), (b) y=√¹ Find the slope and equation of the line tangent to the curve y= 2√x - 8x at x-2 (a) Volume of a cube is increasing at the rate of 20 ft³/min. How fast is the side of the cube increasing when the side is 3 ft ? (b) Find: 4x2y4-4y+5x³-3=0. 6. 7. 8. (a) Using differential find approximate value of √79. (b) If the possible error of the measurment of the radius of a sphere is 20 cm .find approximate error in the measurement of the volume. 9 (a) Solve DE y = 4√x-6x,y(4) = 2 (b) (4√x - 6x) dx.