Thread: critical points

f(x) = 18x + 15x^2 -4x^3 on the interval [-3,4]

A) f(-3) =
f(4) =

B) find the critical points of f(x) state x and y show your work

C) State the absolute maximum and absolute minimum values of the function on the interval [-3,4]


how do i get the critical points iv found the derivative to be 18+30x-12x^2 now what do i do?

Originally Posted by burton6

f(x) = 18x + 15x^2 -4x^3 on the interval [-3,4]

A) f(-3) =
f(4) =

B) find the critical points of f(x) state x and y show your work

C) State the absolute maximum and absolute minimum values of the function on the interval [-3,4]

You can't just post the question.

Where are you having trouble with it? Have you made an attempt? Where is your working?

ow do i get the critical points iv found the derivative to be 18+30x-12x^2 now what do i do?

Originally Posted by burton6

ow do i get the critical points iv found the derivative to be 18+30x-12x^2 now what do i do?

Critical points are points at which the gradient of the function is zero. The gradient of a function f(x) is described by its derivative f'(x), so you're looking for the points at which f'(x) = 0.

So set f'(x) = 0, and solve for x. Once you have the values of x that solve this equation, plug them back into the original equation, f(x), to find the corresponding y values.

Critical numbers are numbers in an interval where f'(c) = 0

So just set the derivative to 0 and solve for the roots. If you can't evenly factor the equation then use the quadratic formula.

It'll make it easier on you if you factor 6 out of f'.

tanks got it