8. Given f(x+ y) = f(x) + f(y) + 2xy for all a, y E R and f'(0) = 0. Find f(0), f'(r), and f(x).

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: = f(x) g(x) If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = y 6…

A: The given graph of the functions is shown as,Let,Note:  As mentioned in the instruction, we are…

Q: Find f(x) such that f'(x) = 6x² f(x) = 2x³ 3x²+2 6x² - 6x and f(2)= 10. - X

A:

Q: Let c =3 If f (x) : Cind f! (0

A: The function given is fx=x2-cx+1 The value of c given is 3. Substitute the value of c in the given…

Q: 2. Given f(x)=x-6, determine whether f'(6) exists.

A:

Q: Let f(7) = -7 and f'(7) = 6. What is gʻ(7) it g(x) = 4+f(x), Enter the answer as a fraction or…

A:

Q: As the number of hours since you ate protein increases from 2 to 2.75 hours what is the average rate…

A: Given: At 2 hours B1=1100 mg/L At 2.75 hours B2=1025 mg/L

Q: = 2. Find f(x) if f'(x) = 7//1 – x2 and f f(x) |

A:

Q: Find a function ƒ(x) such that ƒ'(x) = −8x² + 1 and ƒ(0) = 1 ƒ(x) = |

A: f'(x)=-8x2+1f(0)=1∫xndx=xn+1n+1+c

Q: If f(x) (1)? = 2 x² + 3x x+1 " then what is

A: Given: f(x)=x2+3xx+1

Q: Find a function f(x) such that f'(x)% = - 3a? + 8 and f(0) = 1 f(z) = %3D

A:

Q: Ex. 4) For F and G functions and given that: F(5) =-1,F'(5) =-3 G(5) = 4 G'(5) = 2 a) If P(x)= F(x)·…

A:

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

A: We have,  fx=x3-8x+2           ⋯⋯1

Q: Find the coordinate vector [x]B of the vector x relative to the given basis B. 23) b1 =| b2 and B =…

A:

Q: Suppose that f(x + h) – f(x) = 7hx? – 8hx + 5h²x – 3h? – 7h³. Find f'(x).

A: The quotient difference formula is given as, f'x=limh→0fx+h-fxh it is given that…

Q: If F(x)= f(xf(xf(x))), where f(1) =3, f(3) =5, f '(1)=3, f(3) =4, and f(5) 5, find F (1). F'(1) -

A:

Q: x) such that f"(x)=2r' +3x-4

A: Integration: f''(x)=2x3+3x2-4x+5; f0=2, f1=0 ∫xndx=xn+1n+1+c

Q: The number of houses that can be served by a water pipe varies directly as the square of the…

A: Given that, The number of houses that can be served by a water pipe varies directly as the square of…

Q: Find f such that f'(x) = f(x)= f(16) = 21.

A: Topic:- application of integration

Q: Given that f"(x) and f(1) = 3x² + 2x – 1 and f'(1) = 0 3, find f(x).

A: Given equation is f ”(x) =3x2 + 2x -1 f ’(1) = 0 f (1) =3

Q: Given f (x) = x³ - 3x – 1,x 2 2, find (f~')'(-1)

A:

Q: f"(x) = 7x – 2 - and f'(-3) = –6 and f(-3) -2. Find f'(x) = and find f(4) =

A:

Q: Let f(x) = X x - a Find the value of a so that f'(1) = 1 - 4

A: This question is based on Quotient rule of differentiation.