A function and its first and second derivatives are given below f (x)—2х*+3x*—12х+6 f'(x)=6(x+2)(x-1) 6+12x =(א)''f Use the First Derivative Test to determine whether a critical value occurs at a relative (a) maximum, relative minimum, or neither. Show your work to support your answer! (b) work to support your answer! Determine the intervals upon with f(x) is concave up and concave down. Show your

Q: • Show that both of the functions f(x) = (x − 1)^4 and g(x) = x^3 −3x^2 + 3x+ 2 have stationary…

A: given functions fx=x-14gx=x3-3x2+3x+2 (A) to show both have stationary point at x=1 differentiate…

Q: Let f(x)=x+(1−x)^(1/2) Find the local maximum and minimum values of f using both the first and…

A: For local maxima or minima:The first derivative test is f'(x) = 0The second derivative test…

Q: If f is the function whose graph is shown, let h(x) = f(f(x)) and g(x) = f(x²). Use the graph of f…

A: Given:   Given: hx =ffx  , gx =fx2 To find : h'2 , g'2

Q: let f(x)= X4+1 a find f'() + simplity

A: Givenf(x) = x4 + 1x2

Q: Find the second derivative or f"(x) for f(x) = / 2x + 5. %3D 1 (2x + 5)3/2 (2x + 5)!/2 (2x + 5)3/2…

A:

Q: determine maximums and minimums by the Second Derivative Test, we differentiate y"=72 / (2-8)3…

A: topic  - local maxima and minima

Q: Help find a function f so that f ‘(x) = 3x2+ 2x+5 and f (1) = 10

A:

Q: 9. [Essay] Find the derivative of y * sign 3a* (x? – 3x + 1).

A: Given function is: y=3axx2-3x+1 We have to find the derivative dy/dx. We will use the following…