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. 👍 0
  2. 👎 0
  3. 👁 18
asked by annie

Respond to this Question

First Name

Your Response

Similar Questions

  1. cal

    find the equation of a quadratic function whose graph is tangent at x=1 to the line whose slope8, tangent at x=-2 to solve the line with slope-4 and tangent to the line y=-8 find the equation of the tangent lines at x=1 and x=-2

    asked by erika on February 28, 2011
  2. Calc.

    Find the area of the region bounded by the parabola y=x^2, the tangent line to this parabola at (1,1) and the x-axis. I don't really get what this question is asking. It looks like the area of right triangle to me...try the graph,

    asked by Hebe on September 26, 2006
  3. calculus

    find the equation of a quadratic function whose graph is tangent at x=1 to the line whose slope8, tangent at x=-2 to solve the line with slope-4 and tangent to the line y=-8

    asked by erika on February 28, 2011
  4. 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

    asked by Ray on November 19, 2016
  5. Math (Pre Cal)

    Hi, I am studying for a precalculus quiz and I do not understand this hw problem: "The tangent line to a circle may be defined as the point that intersects a circle in a single point... If the equation of the circle is x^2+y^2=r^2

    asked by Dealie on August 28, 2010
  6. Calculus

    Suppose f(x) is differentiable at x=a. What does tangent line approximation, y=, mean? Select all that apply (A) Local linearization (B) y=f(x)-f(a)-f'(a)(x-a) (C) The best liner approximation of f(x) near a (D) After zooming y is

    asked by George on November 5, 2008
  7. Calculus

    Suppose f(x) is differentiable at x=a. What does tangent line approximation, y=, mean? Select all that apply (A) Local linearization (B) y=f(x)-f(a)-f'(a)(x-a) (C) The best liner approximation of f(x) near a (D) After zooming y is

    asked by George on November 5, 2008
  8. Calculus

    Suppose f(x) is differentiable at x=a. What does tangent line approximation, y=, mean? Select all that apply (A) Local linearization (B) y=f(x)-f(a)-f'(a)(x-a) (C) The best liner approximation of f(x) near a (D) After zooming y is

    asked by George on November 5, 2008
  9. Calculus

    Suppose f(x) is differentiable at x=a. What does tangent line approximation, y=, mean? Select all that apply (A) Local linearization (B) y=f(x)-f(a)-f'(a)(x-a) (C) The best liner approximation of f(x) near a (D) After zooming y is

    asked by George on November 5, 2008
  10. Calculus

    If F(x)=x^3−7x+5, use the limit definition of the derivative to find FŒ(5), then find an equation of the tangent line to the curve y=x^3−7x+5 at the point (5, 95). FŒ(5)= The equation of the tangent line is y = x + .

    asked by Rachael on June 9, 2013
  11. Calculus AB

    Could someone please help me with these tangent line problems? 1) Find the equation of the line tangent to the given curve at the indicated point: 3y^3 + 2x^2 = 5 at a point in the first quadrant where y=1. 2) Show that there is

    asked by Annie on November 25, 2016

More Similar Questions