got a couple of calculus questions

1. What is the equation of the tangent line to y = 2*x(x - 4)^6 at point (5, 10)?

2. If f(x)=8/(x^2+4) , find the slope of the curve at the point (2, 1).

3. The demand function for an item is given by x=200[1-(p/(p+2))] . At what rate is the demand changing when the price p is $8.00 per item?

Which two do you need help with? You did say "a couple"

For question 1, take the derivative of y(x), dy/dx, and calculate its value m at x = 5. Then the equation for your tangent line will be
(y - 10) = m (x - 5).

For question 2, calculate the value of the derivative df/dx at x=2.

For question 3, calculate dx/dp wnen p = 8.

We will be happy to provide further assistance if needed. Please show your work

ok annie, for 1. we are given y(x)and are asked for the tan. line at some point. You do know, or should, that the derivative of y will give us the slope at a point for y. However, I think that the exercise is also expecting you use a theorem. You could expand the poly (x-4)^6, or make use of the theorem for the product of 2 functions. Expanding the poly is tedious unless you can see by observation alone that (x-4)^6 = X^6 - 4x^5 + 16x^4 - 64x^3 + 256x^2 - 1024x +1, as I or an experienced math type can? Thus I think they want you to see y = f(x)g(x) where f = 2x and g = (x-4)^6 and use the product rule. You're text should show that. Substitute 5, the x value, to find the slope. You now have a point and the slope and should be able to handle the equation for the line.
Question 2. is similar, except that the questioner here expects you to know how to handle a function in the denom. Here is a case where it is easier to think of 8/(x^2+4) as being the same as 8(x^2 + 4)^-1 . This simplifies how you might think of the derivative. Once again, evaluate the equation for x = 2 to get the slope. As before, you now have the slope and a point and should be able to go from there.
For 3. you might want to think of x = 200(1 - p(p+2)^(-1)). Use the product rule. Incidentally, in this example the questioner wants you to think of x as the dependent variable. They don't want you to always be thinking of y(x), f(x), etc, but beaware that we can have x(p) too. Find the derivative and evaluate it at p = 8.

hmm.., After review I see I got the constant term in 1. wrong. It should be 4096. As I said, I did that one by 'eyeball' alone only because I know the powers of 2 well. But I think I edited something out and wrote over the constant term. My point however is that I doubt that's what they wanted you to do. Be sure to study the theorems and be alert to where you can apply them.

  1. 👍
  2. 👎
  3. 👁

Respond to this Question

First Name

Your Response

Similar Questions

  1. calculus

    5. Let f be the function given by f(x) = x3- 7x + 6. a. Find the zeros of f b. Write an equation of the line tangent to the graph of f at x = -1 c. Find the x coordinate of the point where the tangent line is parallel to the

  2. calculus

    consider g(x)= {a sin x + b, if x ≤ 2pi} {x^2 - pi x + 2, if x > 2pi} A. Find the values of a a b such that g(x) is a differentiable function. B. Write the equation of the tangent line to g(x) at x = 2pi. C. Use the tangent line

  3. Calculus

    1. On what interval is the function f(x)=x^3-4x^2+5x concave upward? 2. For what values of x dies the graph of f(x)=2x^3-3x^2-6x+87 have a horizontal tangent? Is there no solution because the equation can't be factored? 3. At what

  4. math

    Find the slope m of the tangent line to the graph of the function at the given point and determine an equation of the tangent line. f(x)=7x-5x^2 at (-2,-34) m = ?? y = ?? .

  1. AP Calculus

    Suppose that f has a continuous second derivative for all x, and that f(0)=1, f'(0)=2, and f''(0)=0. A. Does f have an inflection point at x=0? Explain your answer. B. Let g'(x) = (3x^2 + 2)f(x) + (x^3 + 2x + 5)f'(x). The point

  2. Math (Calculus) (mean value theorem emergency)

    Consider the graph of the function f(x)=x^2-x-12 a) Find the equation of the secant line joining the points (-2,-6) and (4,0). I got the equation of the secant line to be y=x-4 b) Use the Mean Value Theorem to determine a point c

  3. calculus

    -find the equation of the tangent line to the curve y=5xcosx at the point (pi,-5pi) -the equation of this tangent line can be written in the form y=mx+b where m= and b= -what is the answer to m and b?

  4. Calculus

    1. use the definition mtan=(f(x)-f(x))/(x-a) to find the SLOPE of the line tangent to the graph of f at P. 2. Determine an equation of the tangent line at P. 3. Given 1 & 2, how would I plot the graph of f and the tangent line at

  1. Calculus

    Use linear approximation, i.e. the tangent line, to approximate 8.4^(1/3) as follows: Let f(x)= x^(1/3) . The equation of the tangent line to f(x) at x=8 can be written in the form y=mx+c where m=1/12 and c=4/3: Using this, find


    Write the equation of the tangent line to the graph of the function at the indicated point. Check the reasonableness of your answer by graphing both the function and the tangent line. Y=(x-2)/(15-x^2) x=-4 HOW DO WE DO THIS

  3. Calculus

    The function g is defined for x>0 with g(1)=2, g'(x)=sin(x+1/x), and g"(x)=(1-1/x^2)cos(x+1/x). A. Find all values of x in the interval 0.12

  4. Geometry Multiple Choice Question Please Help!

    Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale. {THe figure is a circle with a tangent crossing through the top section of the circle. The value of the tangent is 12.

You can view more similar questions or ask a new question.