6) If differentiable functions y = F(x) and y = G(x) both solve the initial value problem dy f(x), y(xo) = yo. on an interval I, must %3! dx F(x) = G(x) for every x in 1? Justify the answer. %3D

Q: Consider the function f (x) = 6x² + 4x + 2. Find F(x) so that F' (x) = f(x). %3|

A: f(x)=6x2+4x+2To find: F(x) such that F'(x)=f(x)

Q: If false state why.

A: Given,

Q: For what value of x does the function g(x) x - 2x concave downward? В. A. x -1 D. x< 2 C. x -2 1/3

A: The graph of y = g (x) is concave downward on those intervals where y = g "(x) &lt; 0.

Q: Find what m equals given tyll-3kyloMyo the differential equation

A:

Q: Question 4. Find f/ (x). (a) f(x) = xsinx (b) f(x) = sech-1x²

A:

Q: f (æ, t) = e-t function fea - fu = 0 provides equality. True False

A: Given the function fx, t=ex-t We need to check the validity of fxx-ftt=0 to get the correct option.

Q: Solve: 2 0 -1 0 2 -6 1 -2 -3 -2 0 1 -5

A:

Q: Let f(x)=√4x² + 4x + 6 f'(x) = f'(5) =

A: To find f'(x)

Q: . Compute f(x) dx ƒ(x) = { 2x if x < 1 4 if x ≥ 1

A:

Q: Q1/ find the derivative of the following function 5x? + 2x+3 f(x) =

A: Explanation of the solution is given below...

Q: 7) Find √ (1/1₂ + 3x + 2) dx

A: Given problem:- ∫4x2+3x+2dx

Q: Question 14 (2) + h(x)]dr 8 1.5 -2/6 -7 -6 Blank 1:

A:

Q: If f(x) = x' – 8x + 2, find f (-4).

A: We have,  fx=x3-8x+2           ⋯⋯1

Q: a) If f (x) = 12x, find f' (27). %3D

A: Solve the function

Q: 10. Find function that satisfies the given conditions: f"(x)=6x³-3x+4, f'(1)=-3, f(1) = -6

A: The function satisfies the condition f''x=6x3-3x+4, f'(1)=-3, f(1)=-6 use the integration formulas,…

Q: f(x) = Tx* +(r*)x+". 3. Find the first and second derivatives of Use exact values in your answers-no…

A:

Q: Compute f(x)dx f(x) = { 2x if x <1 4 if x 21

A:

Q: 6. FinD F(S) if f(t)= t· cost

A:

Q: (vii) If f(1) = 10 and f'(x) > 2 for 1 < x < 4, how small can f(4) possibly be? Give proper…

A:

Q: 2. What is the second derivative of f(x) = - ²x³²x²+6? f"(x) = 5x² - ²³√x f"(x) = 10x + √√√x+6 a. b.…

A:

Q: If f(x)- Vu² - 1 du, then what is f'(3)?

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 4) Suppose that a baseball is tossed straight upward and its height (in feet) as a function of a…

A: (a) Instantaneous velocity and acceleration The height y  of the baseball as a function of time t…

Q: 2. Suppose that f(x) is an unknown function, but we know that g(x) = (x² + 5)(f(x))². (a) Find…

A: Using product rule of derivatives.

Q: Find ƒ′(x) if ƒ(x) = 15e3x

A: Given information: fx=15e3x

Q: 3. Over which interval is the function f (x) = 1 + 2ex -3x increasing?

A:

Q: In each case, find the general solution, using real-valued functions: a. y'"-2y""+y" = 0. b. y" +…

A:

Q: 10) f(x) = x³ + 2 f"(x) = ?

A: Given query is to find the indicated inverse function.

Q: 3. Find the first derivative of the function f(x)= 2x3-4x+1 using forward Difference formula if, X1…

A: Solution: