(Solved): please help me answer these. if you arent going to answer all of them then please just skip.  P ...

Problem 2. Find an equation for the tangent line to the curve y = 2x²+x-3 at x = 4. You must use the definition of derivative instead of shortcut formula to find the slop of the tangent line. Problem 3. Use the formula to find the derivative of below functions. (1) = =(3+2). (2-?5 +2²), (2) g(x) = 52²-7x+2 2³-9 Problem 4. Find the second derivative of below functions. (1) f(x) = 4², (2) g(x) = ln(3x² + 2x - 5). Problem 5. Find the equation for the line tangent to the curve y?=3?-10 at z = 4. Problem 6. A cylindrical container with a diameter of 3 meters is being filled with water. The water is flowing into the container at a rate of 5m³/s. How fast is the water moving up the side of the container? Problem 7. The base of a 50-foot ladder is being pulled away from a wall at a rate of 10 feet per second. How fast is the top of the ladder sliding down the wall at the instant when the base of the ladder is 30 feet from the wall? Problem 8. Find critical numbers of (1) f(x)=³-3x² +1, (2) f(x)=¹/(4-2). Problem 9. Find absolute extreme values for (1) f(x)=³-6x² +5, re [1,5] (2) g(t) = ?t 1+122€ (0, 2). Problem 10. Find the interval where f is increasing or decreasing, and find the local maximum and local minimum for f(x) = 22-24. Problem 11. Discuss the function f(x) = in terms of its concavity, inflection points, and local extreme values.