I have 3 problems I'm struggling with. Any help would be great
1) Given the function below
-Find the equation of the tangent line to the graph of the function at x=1. Answer in mx+b form.
(Now, I found the derivative (100x^2)/(100x^3+25)^2/3. I then plugged 1 in as x and got 4, and when putting it into the point-slope form equation, I get 4x. But for some reason, the test I'm taking is telling me this is wrong, so I'm stumped already.)
The rest goes..
-Use the tangent line to approximate f(1.1).
-Compute the actual value of f(1.1). What is the error between the function value and the linear approximation?
Answer as a positive value only. Approximate to 5 decimal places.
2. Let's explore the function below using the Mean Value Theorem.
f(x)=(7x-21)3There are two x-values where the slope of the tangent line to the graph equals the slope of the secant line between x=0 and x=9. To find them, follow the steps below.
[A] First, find the slope of the secant line between x=0 and x=9.
(With this one, I already know the answer is 9261).
[B] Now, find the derivative of the function.
(I already know this one is 21(7x-21)^2)
C] Set the derivative equal to mSEC and solve. One of these values is x=0, what is the other?
(But with this one, I have no idea where x=0 comes from, and when I set it equal to the slope if get 23/7, which ends up not being correct).
3. box with a square base and open top must have a volume of 70304 cm3. We wish to find the dimensions of the box that minimize the amount of material used.
First, find a formula for the surface area of the box in terms of only x, the length of one side of the square base.
[Hint: use the volume formula to express the height of the box in terms of x.]
Simplify your formula as much as possible.
(With this one, I need A(x), A'(x), A"(x), and the evaluation of A"(x) at the x value where A'(x) = 0)
Pleeeasse help. If you can help with any, I would be in your debt for sure!