Thread: Help finding the derivative of a function given the extrema and horizontal tangents?

create an expression for the derivative of a function such that the function has horizontal tangents at x=-2, x=0 and x=3. The function should have relative maxima at x=-2 and x=3 and a relative minimum at x=0.

I am also confused by the way the question is worded .. when they say the function has all these tangents do they want you to find the function that fits all these descriptions and then find the derivative of that function for the final answer? I'm still unsure how to go about solving this .. i found when the function is increasing and decreasing but the only expression i could think of was f(x) = x(x+2)(x-3) but this doesn't satisfy the positive or negative values when needed for either increasing or decreasing parts of the function. HELP!

Originally Posted by yess

create an expression for the derivative of a function such that the function has horizontal tangents at x=-2, x=0 and x=3. The function should have relative maxima at x=-2 and x=3 and a relative minimum at x=0.

I am also confused by the way the question is worded .. when they say the function has all these tangents do they want you to find the function that fits all these descriptions and then find the derivative of that function for the final answer? I'm still unsure how to go about solving this .. i found when the function is increasing and decreasing but the only expression i could think of was f(x) = x(x+2)(x-3) but this doesn't satisfy the positive or negative values when needed for either increasing or decreasing parts of the function. HELP!

f'(x) = ax(x + 2)(x - 3). Integrate to get f(x). Choose the value of a so that the resulting quartic approaches -oo as x approaches +oo or -oo.