Question

generate a continuous and differentiable function with the following properties: f(x) is decreasing at x=-5, local minimum is x=-3, local maximum is x=3

Answer 1

Since, there is local minimum is x=-3, local maximum is x=3

so, derivative must be zero at x=-3 and x=3

we can set up derivative as

we are given f'(x) is negative at x=-5

so,

so, 'a' must be negative

Let's assume a=-1

now, we can find f(x)

Let's assume C=0

so, we get

............Answer