Consider the graph of the function f given below. f(x) I -2 4 B) If h(x) 2 0 -2 2 x 4 A) If g(x) = xƒ(x), calculate g' (3). [Select] x² f(x)' C) If i(x) = x² ƒ(x), calculate i” (−1). [Select] calculate h' (-1). [Select]

Q: -7 -6 -5 -4 -3 1 2 3 J 4 5

A: We have a graph of f(x)We have to sketch graph of f'(x)

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Q: Differentiate the following function. f(x) = e - 2x2 - 4x d (e -2x2 - 4x) - 2² - *x) = [ dx

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A: Given that to he function f is one-to-one function.

Q: Consider the function:-- f (x) = 1/2 x2   Sketch a possible graph of f' .

A: Given function is fx=12x2. To sketch a possible graph of f'. Solution: Differentiating the given…

Q: Use the following graph of the function f(x) to draw f'(x) and f''(x).

A: Given: Graph of the function f(x) is shown as:

Q: Find the function ƒ with the following properties. ƒ'(x) = 3x2 - 1; ƒ(0) = 10

A: Given, f'x=3x2-1f0=10

Q: the graph alongside to find

A:

Q: h (x) = x" – xV2

A: We have to differentiate the function: hx=xπ-x2 We know the formula of differentiation,…

Q: Determine all values of x for which the slope of the line tangent to y=x³ - 4x² +9x-1 is 5.

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Q: ☐ ☐ 4. The figure below shows the graphs of f(x), f'(x), and f" (x). Identify each curve. blue black…

A: Step 1:Step 2: Step 3: Step 4:

Q: Find the general form of f if f'(x) = 10f(x).

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Q: Suppose that the slope of the line tangent to the graph of a function f at the point (x, f(x)) is…

A: Using integration.

Q: 9. Find the slope of f(x) = (x+2)2 +5 at the point (3,-4)

A: