The function f(x) is defined as follows: f(x) = 1 2x + b if x ≤ 1 (2x − 1)² if x>1 - Use a mathematical sound argument to find all possible constants b such that fis differentiable at x = 1.

Q: Consider the function f(x) = x13 + 9x – 4. = 0. State any theorems a. Show that the function f(x)…

A:

Q: ) Is the function f(x) = differentiable on the open interval (-1,1)? x².

A:

Q: For the function f (x) = 2-x² – x² +x, (a) List the x values where = 0. (b) Are all of these values…

A: Consider the given function, f(x)=2x4-x2+x Find the first derivative of the given function,…

Q: Let f(x) = m1x + a and g(x) = m2x + b, where m1, m2, a, and b are constants. Determine the necessary…

A: f∘g=g∘ffgx=gfxfm2x+b=gm1x+am1m2x+b+a=m2m1x+a+bm1m2x+m1b+a=m1m2x+m2a+bm1b-b=m2a-abm1-1=am2-1

Q: Let f be the function given by f(x) = Jax + b for x 2 where a and b are constants

A:

Q: 1 g(x) = /3 — х

A:

Q: Find x-intercepts of the function: x2 – 9 f (x) = Зх + 1 Select one: O a.x = 3 O b.x= -3, x= 3 C. X=…

A:

Q: Consider the following piecewise-defined function: f(x) = { 4-ax² if x ≤1 b 2x if x > 1 Find the…

A: Ans :Now we need to sketch the graph in the interval [-3,3]Firstly let's find some points on the…

Q: Let f(x) = 1+ V7x +1. Determine the largest possible domain of f(x) Select one: • [-1/7, +o0)

A: Given function is  fx=1+7x+1

Q: Plot f (x) = 2√x − x on [0, 4] and determine the maximum value graphically. Then verify your answer…

A:

Q: The function x2 f(x) = 1 - x is decreasing on (0, 1). Select one: O True O False

A:

Q: For the function, f(x) = 2sin²x - 3sin x, 0<x< 2n , find the following algebraically: /플) =D N플)=D…

A:

Q: Consider the function f(x) = 1 + 2x + 3x² + 4x³. Let s be the sum of all distinct real roots of f(x)…

A: First derivative check for monotonicity

Q: Use Intermediate Value Theorem to check whether f(x) x- 2x -1 has at least one zero between x= -1…

A:

Q: The function f(x)=(x2+9)/(x2+12) concave up on the interval (a,b). What si the maximum of b-a? 2 4 6…

A:

Q: Let f (x) = 2x3 - 3x2 - 36x + 14. Also, let a = 0 and b = 1. (a) Show that the function f is…

A: