Suppose f is defined on [a, b] and g is defined on [b, c] with f(b) g(b). Then define { f(x) if a < x < b, h(x) = g(x) if b

Q: -What is the derivative of (x + 1)2 ? a) x? + 2 b) x c) x d) 2x+2

A: We will use chain rule of derivative

Q: Suppose f: (a, b) →→ R is differentiable. True or false: If f is unbounded, then f' (the derivative…

A: f:a, b→ℝ is differentiable.

Q: Let f(x) = 2x² + 1. Use the limit definition of the derivative to find f'(x).

A:

Q: tion f defined as xy Ax, y)=- when (x, y)#(0, 0) when (x, y)=(0, 0) =0, is continuous at the origin.

A:

Q: Consider a quadratic function f(x) = ax?+ bx + c, where a, b, CER and a # 0. She hat the tangent…

A: f(x)=ax2+bx+climit definition of derivative states that :f'(x) =limh→0f(x+h)-f(x)hf'(x) =limh→0…

Q: Consider the function f(x) = In (x - 4) a.) Use the First Derivative Test or the Second Derivative…

A:

Q: Which of the following statements is false for a function f that can be differentiated at least…

A: We have to define which statement is wrong

Q: Let f: A →B and g: B →C be functions. Suppose that f and g have inverses. Prove that g ◦ f has an…

A:

Q: The line normal to the graph of f at the point (1,2) passes through the point (-1,1).  Which of the…

A: Topic = Functions

Q: 6. Consider the DERIVATIVE f' graphed below. Sketch a possible graph of the original function f on…

A:

Q: # 19, 20, 23) Find the derivative of each of the following functions using the definition of…

A:

Q: Suppose f is a function that satisfies the equation f(x + y) = f(x) + f(y) + x2y + xy2 for all real…

A:

Q: -3 -2 -i O Graph of f' The graph of f', the derivative of the function f, is shown above. On which…

A: We know that, Let f ' be the first derivative of function f that is differentiable on a given…

Q: 7. Show that if f is a function of r only, then 0²ƒ(r) = f'(r) + ²ƒ'(r)

A: The given data is: Show that if f is a function of r only, then ∇2fr=f''r+2rf'r