12. The function f(x) and its first and second derivatives are as given below. 1-x x² (a) Domain of f(x) is (b) y-intercept is f(x) = x-2 f'(x) = ²-² f"(x) = x3 (c) Horizontal asymptote(s) is (d) Vertical asymptote(s) is and x-intercept is (e) Find the local maximum and local minimum. (f) Find the inflection points. 6-2x x4

Q: (a) State the values of x for which f'(x) does not exist. (b) Sketch the graph of y = f'(x) on the…

A:

Q: Consider the function h(x), for which h(2) = − 1 and h'(2) = -6. Find f'(2) for the function f(x):…

A:

Q: dy dx (b) y = (x³ - 2x + 8) (x² + 4) 1. Use the Differentiation Rules to find (a) y = 6x³ + 3x√x -…

A: Since you have posted a multiple question according to guildlines I will solve first(Q1)   question…

Q: graph F(X), Determine f'(x) then graph T] f(x) = 1 + x + x

A:

Q: 2) Find the tangent equation for the function f(x) = x² + 5x at the point (1,4). *****: **********

A:

Q: Find the derivative of g(x) = x² ex

A:

Q: 2. (a) Sketch the graph of y = f'(x) given the graph of y = f(x). (b) Specify the domain and range…

A: Graph

Q: Find the indicated quantities for f(x) = 2x. (A) The slope of the secant line through the points…

A:

Q: Find the indicated derivative for y=f(x)=9-x^2

A: Answer and explanation is given below...

Q: 1. (a) For the function f(x)=x* - x² (whose %3| | graph is shown) use the power rule to take…

A:

Q: Let P(x) = F(x)G(x) and Q(x) = F(x)/G(x), where F and G are the functions whose graphs are shown F G…

A:

Q: Given the graph of y = f(x) sketch the graph of f'(x) 2 -2 -2

A: Given: The graph of fx as follows:   To sketch: The graph of f'x

Q: Explain in your own words, how do you find the followings using first and second derivatives of…

A: To Explain: How can we find followings using first and second derivatives of function f(x):(a)…

Q: How and why does the concavity of f(x) affect the positive and negative intervals of f''(x)?  How…

A: if the concave is up then f'(x) is increasing and f"(x) will also be increasing and concave will be…

Q: From the graph of f(x), determine the graph of f'(x). -6 i पं -3 -2 1 y 5 4 3 2 O -1 -2 -3 -4 -5 2 W…

A: We need to find graph of f'(x) from given graph of f(x).Concept -If f(x) is increasing then slope…

Q: The derivative of a function is g'(x) = 19 – 6x² and the graph of g(x) passes through the point P(3,…

A: To find  g(x)