The following is a table of values of the functions f, g, f' et g': a) If h(a) b) If H(z) a) h'(2) = b) H'(2) - f(g(x)), find h'(2). g(f(z)), find H'(2).

Q: If f(x) 3 find f'(2). x²

A: Given that f(x)=3x2So, f(x)=3x-2

Q: Let f and g be functions such that f(0) = 3, g(0) = 5, f' (0) = 4, g'(0) = -3. Find h'(0) for the…

A: Given f0=3,    g0=5f'0=4,   g'0=-3hx=gxfx To find h'0

Q: Suppose g(x) = x²f(x) and it is known that f(2) = 5 and f'(2) = -2. Evaluate g'(2). g'(2) =

A:

Q: Let f(x) be a one-to-one function such that f(2)=5 and f'(2)=-4.  Find f(-1)'(5)

A:

Q: Find f'(2) if y = f(x) is the nonnegative function defined for x, y > 0 by the equation x" = y?.

A: To find f’ (2), if y = f (x).

Q: Construct the table of signs for f'(x) and f"(x) ginve f(x)= x4ex on its domain of (-inf, +inf)

A:

Q: If f is one-to-one and f(1) = 5, f(3) = 7, and f(8) : - 10, find f-'(7), ƒ¯'(5), and f¯'(-10).

A: f is one to one and given  f(1)=5    therefore f-1(5)=1 f(3)=7    therefore f-1(7)=3 f(8)=-10…

Q: If f'(x) = x(x- 2)(x+1), then the graph of f has points of inflec- tion when x = A. -2 and 1 B. 2…

A: f''(x)= x(x-2)(x+1)2  To find the points of inflection of function f  A. -2 and 1 B. 2 and -1 C. 2…

Q: Let F(x) = f(x³) and G(x) = (f(x))5 . You also know that aª = 14, f(a) = 3, f'(a) = 13, f'(a³) = 14.…

A: Since we have the expression of F(x) and G(x) in terms of f(x), to find the derivative of both F(x)…

Q: A B C D E F f(x) X

A: To determine the points at which exactly two of fx, f'x and f''x are zero.

Q: Let f and g be the functions in the table below. g(x) 2 3 1 X 1 2 3 f(x) 3 1 2 (a) If F(x) =…

A:

Q: x2 Find f'(x) if f(x) = 5x – 3

A: As we know that: The Quotient rule: fg'=f'·g-g'·fg2 The Power rule: ddx(xn)=nxn-1 Given: f(x)=x25x-3

Q: Find the derivative.

A: To compute the derivatives of the composite functions from the given data

Q: if f''(x) = 0 an inflection point, what can be said aboutthe sign of  f'''(x)?

A: We have to fund the condition for f"' (x) for a inflection point  to happen.

Q: Find the original function f(x) from given equation f'''(x)

A: We can solve this as follows:

Q: Let F(x) = f(x5) and G(x) = (ƒ(x))5 . You also know that aª Then F'(a): = = = 8, f(a) = 2, ƒ'(a) =…

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Q: For the function f(x) = (x + 4)*, find f''(x), f''(0), f''(2), and f'"(- 3). f"(x) = D Select the…

A: Given function fx=x+44 The first derivative of given function is f'x=4x+43 The second derivative of…

Q: point) If ƒ(5) = -3, g(5) = -4, f'(5) = -2, and g'(5) = -2, find the values of the following: %3D (f…

A:

Q: The functions f and g are differentiable and h(x) = f(g(x)). Use the information below to find…

A: We know that If h(x)=f(g(x)) then h'(x)=f'(g(x))g'(x)

Q: Suppose that for two functions f & g, we know the following information:f(8) = 16f'(8) = 6f(3) =…

A: The given composition function is

Q: Suppose that f(-4)=3, f'(-4)=0, g(-4)=3, g'(-4) = 4. Use this to compute (f•g)'(-4)

A:

Q: Find the derivative

A:

Q: 2. Find the derivative of each function a) f(x) = x³e/x et3+7 b) g(t) %3D t2 )듬x리 In(2x + 1) 8x+9 x3

A: According to our guidelines we can only answer 3 subparts of a question, rest you can repost