Can you please help mw with these calculus 1 (math 1401) chapter 4 and 5 problems. please do all the problems and show your work

6. Making use of the 1st and 2nd Derivative Tests, find all local extrema, intervals of increasing and decreasing, intervals of concavity, critical points, and inflection points of f (x) = 2 - +x+1. 20pts 7. Examine h(x) = x3 - 3x2 + 2x and answer the following: a. Verify that you can use the Mean Value Theorem on the interval [0,1], and if so, what value(s) are guaranteed to exist? b. Verify that you can use Rolle's Theorem on the interval [0,2], and if so, what value(s) are guaranteed to exist? 10pts If you are looking for the bonus, you've looked too far. 8. Write the equation of L(x) that represents the linear approximation for f (x) = 13x-3 x+1 - at a = 1. Use L(x) to approximate the value of f (x) at x = 1.2. 15pts 9. Evaluate _3 (6x2 - 7)dx 10pts 10. Evaluate ( x5 + 5 + 2 - -)dx 15pts 11. Evaluate S(x5 + 6)'x* dx 10pts 12. Evaluate Jo V35 * dx 15pts Vx 2 + 1