Thread: Some calc questions! need help

1. Some calc questions! need help

Find the critical numbers of f(x)=x^4(x-3)^3

Find any absolute or local maximum and minimum values of f(x)=8-2x if x> 6.

Evaluate f(x)=sin(x^2), and tell whether its antiderivative F is increasing or decreasing at the point x = -4 radians.

Find critical numbers of function
y=5x^2+20x

How many points of infelction are on the graph of the function
f(x)=12x^3+14x^2-7x-9

Find the maximum or minimum points of the function
f(x)=(1-x^2)^2 +6x^2

Find f
f
"(x)=12x+24x^2

Find the smallest possible area of an isoceles triangle that is circumscribed about a circle of radius r.

2. Originally Posted by eyesofwar
1) Find the critical numbers of f(x)=x^4(x-3)^3
Take the derivative (you'll need to use the Product Rule and the Power Rule). Set the derivative equal to zero. Solve for the critical points.

Originally Posted by eyesofwar
2) Find any absolute or local maximum and minimum values of f(x)=8-2x if x> 6.
Follow the process in (1) to find the critical points, but ignore any x-values that are less than six. Also test the function at x = 6, to see if you get an absolute min/max value.

Originally Posted by eyesofwar
3) Evaluate f(x)=sin(x^2), and tell whether its antiderivative F is increasing or decreasing at the point x = -4 radians.
The antiderivative g(x) of f(x) is the function such that g'(x) = f(x). That is, f(x) gives the slope of its antiderivative!

Use this fact to find the sign of the slope of the antiderivative at x = -4.

Originally Posted by eyesofwar
4) Find critical numbers of function y=5x^2+20x
This one works just like (1) above.

Originally Posted by eyesofwar
5) How many points of infelction are on the graph of the function f(x)=12x^3+14x^2-7x-9
For this, you'll need to find the first and second derivatives. Points of inflection are zeroes of the second derivative at which the sign of the second derivative changes. So check for this.

Originally Posted by eyesofwar
6) Find the maximum or minimum points of the function f(x)=(1-x^2)^2 +6x^2
First find the critical points (as in (1) above). Then use whatever tests you've been given (such as the Second Derivative Test, or intervals of sign, or graphing, etc) to determine the sort of point (on the original function) that is indicated by the critical points (of the derivative of the original function).

Originally Posted by eyesofwar
7) Find f
f
"(x)=12x+24x^2
I'm sorry, but I don't understand what is being asked for here...? What is meant by "finding f f"(x)=..."?

Originally Posted by eyesofwar
8) Find the smallest possible area of an isoceles triangle that is circumscribed about a circle of radius r.
Draw the circle. Draw the triangle around the circle, with its sides touching the circle. Draw a radius line from the center to where one of the equal-length sides meets the circle, and label as "r".

Since the smallest possible triangle will obviously touch the circle with all three sides, make sure you've drawn the base of the triangle as touching the circle, too. Draw a radius line down to this intersection point, labelling as "r".

Draw in the rest of the altitude line for the triangle, labelling the rest of the height as "h", so the total altitude is h + r.

Where you go from here may depend on how much you remember from geometry. What are your thoughts? How far can you get?