Can you please help me solve 15, 21, and 24. Thanks so much! :)

property. 17. Use the Intermediate Value Theorem to show that the equation x6 - 8x4+ 10x2 - 1 = 0 has at least six distinct solutions. 25. Jump the IVT In Exercises 18-20, determine whether or not the IVT applies to show that 26. Jump the given function takes on all values between f(a) and f(b) for x E [a, b]. on [0, 4] If it does not apply, determine any values between f(a) and f(b) that the cannot function does not take on for x E [a, b]. 27. Infinite of the IVT 18. a num f ( x ) = x for x 0 for the interval [-1, 1]. IVT on [0, 4 (b) is no 29. C 19. have any roc e oppos f ( x ) = - X for x 0 bottom. At the reached the bo Jacqueline rea 21. Carry out three steps of the Bisection Method for f(x) = 2* - x3 as that there was ISHOWS: 32. On f (5) = 10 (a) Show that f has a zero in [1, 1.5]. barometric pres s true, ner (b) Show that f has a zero in [1.25, 1.5]. system was pas (c) Determine whether [1.25, 1.375] or [1.375, 1.5] contains a zero. Thursday the st mb, while the 22. Figure 6 shows that f(x) = x - 8x - 1 has a root in the interval risen to 1014 n [2.75, 3]. Apply the Bisection Method twice to find an interval of length a time between Buffalo had the 16 containing this root. Further Insights and Challenges Exercises 33 and 34, address the 1-Dimensional Brouwer Fixed Point The- orem. It indicates that every continuous function f mapping the closed in- terval [0, 1] to itself must have a fixed point; that is, a point c such that f ( c ) = c. 33. Show that if f is continuous and 0 2. 13. 2* + 3* = 4* has a solution. 14. cos x = cos x has a solution in (0, 1). 15 ex + In x = 0 has a solution. 16. tan x cos x has a solution. 17. Use the Intermediate Value Theorem to show x6 - 8x4 + 10x2 - 1 = 0 has at least six distinct solut In Exercises 18-20, determine whether or not the IVT the given function takes on all values between f(a) and If it does not apply, determine any values between f function does not take on for x E [a, b]. 18. kip x for x 0 aber the interval [- 1