+ X m125 - Section 3.9 (2021) - Math VA X Feedback fo webassign.net/web/Student/Assignment-Responses/last?dep=2786834 4 Points] DETAILS One use of linear approximation is to solve certain equations where no algebraic methods apply. This problem illustrates that use. follow the steps below. (a) Find the linearization of e * + x near 0. e 2 + X ~ (b) The equation ex + x = 2 has a solution near x = 0 . To approximate the solution, first create a new equation by replacing the left side of this equation with linearization that you found in part (a). Write this new equation here. Now solve the new equation. X (c) Based on your work above, we can say that the equation ed+ x = 2 has an approximate solution X ~ 8:57 ACTAULC ~ ENG 10/3/ Type here to search+ X m125 - Section 3.9 (2021) - Math webassign.net/web/Student/Assignment-Response [-/1.5 Points] DETAILS (a) Given that f(7) = 18, and f '(7) = -1.3 , estimate f(7.1). Give your answer to two decimal places. f ( 7 . 1 ) ~ (b) Suppose we also know that f "(x) > 0 for all x. Does this make your answer in part (a) an under-estimate or over-estimate? O Under-estimate O Over-estimate 6. [-/3 Points] DETAILS Suppose f'(x) is a differentiable decreasing function for all x. In each of the following pairs, which number is the larger? (a) f'(8) and f'(9) Of'(8) is larger Of'(9) is largerX V + X m125 - Section 3.9 (2021) - Mati A webassign.net/web/Student/Assignment-Response 6. [-/3 Points] DETAILS Suppose f'(x) is a differentiable decreasing function for all x. In each of the following pairs, which number is the larger? (a) f'(8) and f'(9) O f'(8) is larger Of'(9) is larger (b) f" (8) and 0 Of"( 8) is larger O 0 is larger ( c ) f (8 + Ax ) and f' ( 8 ) Ax + f ( 8 ) O f (8 + Ax) is larger Of' ( 8 ) Ax + f ( 8 ) is larger 7. [-/2 Points] DETAILS Provided certain hypotheses are met, the Mean Value Theorem relates the average rate of change of a function over an interval with the insta point in that interval. Type here to search