Assume Y is continuous on [c, d] and differentiable on (c,d). (a) If y is non-decreasing (monotone increasing) is it true that y'≥ 0? (Either prove your answer or give a counterexample). (b) If y is strictly increasing, is it true that y'> 0? Either give a counterexample and show where the proof of (a) fails or prove your statement.

Q: 4. (5pt) If f(r) = [t – 1) cosh t dt, on what interval is ƒ increasing? (Hint: Use the Fundamental…

A:

Q: Suppose f"(x) = (x + 2)°(x + 1)²(x – 2). Which of the following statements about the curv y = f(x)…

A: If f"(x) > 0 , curve is concave up If f"(x) < 0 , curve is concave down So only check the sign…

Q: If f(x) is continuous at x = c then f'(c) exists. True False

A:

Q: (6) . that Let f(x) be a differentiable function on the interval (0, 0) such f (x*) = 3f(x), for…

A: We have to prove the given equation.

Q: If G(x,y) is differentiable with respect to x and y then it is always possible to find the number…

A:

Q: How would you remove the dis . z46 f(r) =

A:

Q: Use the Second Fundamental Theorem of Calculus to find F'(x). • L₁ VE 4 + 4 dt Vt Step 1 F(x) = Note…

A:

Q: Assume ƒ is a continuous on [2, 4],, and ƒ(2)= 4. Evaluate ƒ(4).

A: we have been given that f is continuous on [2,4] and f(2)=4. we have to evaluate f(4). the given…

Q: How close to 0 we need to take x so that lnx0 but f(0) does not exist

A:

Q: 7. Show that if f is differentiable on (a, b), and f'(c) > 0, where ce (a, b) and if f' is…

A:

Q: 2. a) Give an example of a function f: R →R that is differentiable everywhere and 1- to-1, but f'(x)…

A: Let, f(x) = x3 .      Then, f(x), being a polynomial, is differentiable for all x ∈ R, i.e.,…

Q: Explain why or why not Determine whether the following statements are true and give an explanation…

A: We have to determine whether the given statements are true or not: a.  ∫fx f'x dx=12fx2+Cb.  ∫fxn…

Q: each

A:

Q: Suoppose that f is a differentiable function satisfying the following differential equation: (*) f"…

A:

Q: If f and g are differentiable functions on (-oo, o0), then y = f(g(x)) is differentiable everywhere…

A: This question related to derivative.

Q: Let a differentiable function z = f(h²(x² + y3), 2łn(x +y)) satisfying the condition f(4,0) 1 be…

A: We need to find the partial derivative of z with respect to x for the given function.

Q: be de by 8 <x3 + y3 f(x, y) = x2 + y2 if (x, y) = (0, 0) if (x, y) = (0, 0). %3D (a) Is f continuous…

A: Note- Since you have posted a question with multiple sub-parts, we will solve first three sub-parts…

Q: If fCxl is continuous on [2,7],then Si f(u) dvz f (7)-(2) True e or false?

A: we have given that f(x) is continuous on[2,7].

Q: 7. Where is f(x.y)= continuous? Do not just write an answer, show your work or give any necessary…

A:

Q: suppose f (x) = Vx (x>0),prove that f is differentiable (0,00) and find f'(x) on

A: Function f(x) = √x (x&gt;0)  We know f(x) =Xn

Q: If f is continuous on [a,b], then f(x)dx= π + A) True B) False f(x) dx

A: Given that f is continuous on a,b. ∫abπ fx dx = π ∫abfx dx Say that the statement is true or false.…

Q: (5) Prove that if f is continuously differentiable on [a, b], then |f(a) – f(b)| a – b max f'(x)|…

A:

Q: the answer quickl

A: