Generate a continuous and differentiable function f(x) with the following properties:

Question

•f(x) is decreasing at x = -5

•f(x) has a local minimum at x = -2

•f(x) has a local maximum at x = 2

Answer 1

f'(5) < 0

the critical points are:

f'(-2) = 0

f'(2) = 0

So then

y' = (x+2)(2-x)

= 2x + 4 - x^2 - 2x

= 4 - x^2

integrating:

y = 4x - (1/3)x^3 + c

you can graph this function and

it's derivative at

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add a slider for c;

even for c=0, the function possesses

these properties