SOLVE APPLICATIONS OF DERIVATIVES CALCULUS

1. Find the equation of the line tangent to the curve y=3x"3 + 6x @ (Oil J. The line also intersects @ (6,8). 10. A spherical balloon is inflated with gas @ a rate of 900 CU Ch'i/min. How fast is the radius Changing when the radius is 12 cm? 2. Find the equation of the tangent line to the curve y=2x^2 + 3, that is parallel to the line 8x - y + 3=0.3. Find the equation of the tangent line and normal line to the curve y = x^2 - 4x -5 @ (-2,7).4. 40 linear meters cyclone wire is used to enclose a rectangular garden. Find the largest area that can be enclosed with this fencing and calculate the dimensions of the lot. Answer with text and/'or attachments: 5. The sum of one number and three times the other number is a minimum and the product of these two positive numbers is 50. Find the numbers.6. A student throws a ball upward from a height of 48 feet @ a rate of 32 feet per sec. Using the equation h= -i 6(t"2) +{V0)t + H0, where V0 is the initial velocity and He, the starting elevation. find the maximum height otthe ball. 7. Two cars; one going east @ the rate of 55 fps and the other going south @ 44fsz are traveling toward an intersection of their two roads. At what rate are the two cars approaching each other at the instant when the first car is 400 feet and the second car is 300 feet from the intersection? 8. A right circular cone having a radius that is half the height, enlarges at the rate of 5 cu. cm per sec. How fast is the volume of the cone changing when the radius is 8 cm?9. The volume of a sphere is increasing at a constant rate of 12.8pi cu cm/s. Find the radius at the instant when the radius is increasing @ 0.20 cm/s