Im having issue solving Question 4 and 5. Need explanation as well with the solution

all Fido 8:48 PM 7 82% C O inst-fs-yul-prod.inscloudgate.net 1 of 1 MAT135HIF Calculus 1 Assignment 8 Due Monday June 8 at 11:45 pm (to be submitted on Crowdmark) Notes: Due to time limitations, only some questions may be graded. The assignment will be graded based on not only correctness and completeness, but also clarity and co- herence. Unless otherwise indicated, all answers need to be justified. While not needed or recommended, you may use a basic calculator. Unless otherwise indicated, the use of more advanced calculators (which for instance may handle variables, solve equations, or plot graphs) is not allowed. Answers without justification may get zero. 1. Use the linearization to estimate the value of the function at a point near the center of the linearization and determine if your approximation is an overestimate or an underestimate: (a) Approximate elf at x = 1.1 with center of linearization a = 1. (b) Approximate In(x' + 1) at x = 2.2 with center of linearization a = 2. 2. How many solutions does et - x2 = 0 have? Why? (Do not use the graph.) 3. Determine the intervals where the following functions are concave up or concave down: (Do not use the graph.) (a) x3 - 5x + 2 (b) x' + 10x3 + 20x2 + 25x +2 4. Prove that for all x 2 0 and all positive integers n, e* 2 1 + x + +. 5. Let f(x) = In(x3 + x + e). (a) Show that f is invertible (on its domain). (b) Is f differentiable at 1? If yes, find (f-1)'(1). 6. Find the slope of the line tangent to the curve defined by the equation y' + xy' = x(x - 1)2 at the point P = (-1, 2). (Note that P is on the curve.) K