x f(x) f'(x) g(x) g'(x) 34 1 6 1 4 -2 -6 1 3 5 1 3 3 6 5 1 3 -2 4 The functions f and g have continuous derivatives. The table gives values of f, f', g, and g' at selected values of x. Part A: Find h'(3) if h(x) = g(f(x)). Part B: Find m'(2) if m(x) = f(x²). Part C: Let K(x) = f(g(x)). Write an equation for the line tangent to the graph of k at x = 6. g(x) f(x) Part D: Let j(x)= Find /(4).

Q: 1. Using Definition of Derivative to find f'(x): a) f(x) = 2x² b) f(x) = x³ c) f(x)=√x+1 d) f(x) ==…

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Q: A function f satisfies the following conditions. f(-3) = 2, f' (-3) = 0, f(-1) = 5, f' (-1) = 0, f…

A: Given that the function f satisfies the following conditions f(-3) = 2, f'(-3) = 0, f(-1) = 5,…

Q: Find the first and second derivatives of the function. f(x) = f'(x) = f"(x) = Identify the intervals…

A: Given function, f(x)=x2+x2

Q: Make a sign diagram for the derivative of the function. f(x) = x² + 4x³8x² + 52 f'(x) ? 0 f'(x) ?0 X…

A: The given function is

Q: Use the graph of f and g. p(x) = f(x)g(x) f(x) q(x) = g(x) y 12 10 8 6 2 -2 6 8 10 (a) Find p'(4).…

A: a) Given that p(x)=f(x)g(x)So, p'(x)=f'(x)g(x)+f(x)g'(x) [product rule]We plug…

Q: A table of values for f, g, f', and g is given below. xf(x) g(x) f'(x) g(x) 1 2 3 2 3 1 3 1 3 3 1 3…

A: (A) The derivative h'x can be represented as follows: h'x=f'gx·g'x

Q: x)G(x) and Q(x) = F(x)/G(x), where F and

A: here f(3) = 4;     f(8) = 5; write the equation of function f(x) from point(3,4) to (8,5).  y = mx…

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: (a) Let h(x) = f(x)/g(x). Find h'(1). (b) Let h(x) = g(f(x)). Find h'(-1).

A: Definition used -           Quotient rule of derivative -…

Q: Make a sign diagram for the derivative of the function. f(x)=x+4x38x² +62 f'(x) [ increase 0…

A: Introduction: Any interval in the domain of a function's derivative can be utilized to assess…

Q: Consider the function, whose graph y = f(x) is shown below. -3 -2 What is the set of values of x E…

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