College Math

2008 (2nd)Course2-4.1
We are to find a function f(x) such that its derivative is x^2+x-1 and the graph of y=f(x) is tangent to the straight line y=x+1.
First we find the coordinates of the point at which y=f(x) and y=x+1 are tangent.Since the slope of the tangent line is A,the x-coordinate of this point satisfies
x^2+x-B=0.
Therefore,the x-coordinate of this point is either CD or E,and hence the required point is either
(CD,FG) or (E,H).
Hence the required function f(x) is either
y=f(x)=1/Ix^3+1/Jx^2-x-K/L .......#1
or
y=f(x)=1/Ix^3+1/Jx^2-x+MN/O .......#2
Furthermore,since the graph of #1 can be obtained by translating the graph of #2 in the direction of the y-axis,the area of the region bounded by the graphs of #1 and #2 and the two straight lines x=CD and x=E is PQ/2.

  1. 👍 0
  2. 👎 0
  3. 👁 236

Respond to this Question

First Name

Your Response

Similar Questions

  1. Calculus

    R=M^2(c/2-m/3) dR/dM=CM-M^2 I found the derivative. Now how would I find the vale of M that maximize the derivative dR/dM? set it to zero, and solve for m. You get two solutions. Use the second derivative to see which one is the

    asked by Anonymous on May 29, 2007
  2. Calculus. I need help!

    Write the composite function in the form f(g(x)). [Identify the inner function u=g(x) and the outer function y=f(u).] Then find the derivative dy/dx. y=√sinx √ is square root.

    asked by danny on February 25, 2012
  3. Calculus (Continuity and Differentiability)

    Okay. So I am given a graph of a derivative. From what I can gather, it looks like the function might be abs(x-2)-4. (I was not given an explicit function for g', just its graph.) The question then goes on to ask me: Is it

    asked by Mishaka on November 12, 2011
  4. MATH

    We now have d dx [x5 + y8] = 5x4 + 8y7y' = d dx [9] = 0. Rearranging this, we get 8y7y' = ?????????? ------------------------------------- A table of values for f, g, f ', and g' is given. x f(x) g(x) f '(x) g'(x) 1 3 2 4 6 2 1 8

    asked by Anonymous on October 6, 2014
  5. calculus

    Find the derivative of the function using the definition of derivative. g(t)= 9/sqrt(t) g'(t)= state the domain of the function and the domain of the derivative (use interval notation)

    asked by maura urgent!! on September 19, 2012
  1. calculus

    1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))? 2. Find the derivative of f(x) = |x + 2| at the point (1, 3) 3. Find f '(x) for f(x) = -2x3 + 3x2 - x + 15. 4.

    asked by mock on January 15, 2015
  2. Math

    Find the intervals on which the function is increasing, decreasing, concave up, or concave down and find any local extreme values and inflection points. So I know how to do the above, but not with piece wise functions. Someone

    asked by Beth on February 3, 2016
  3. Calculus

    Given the function: f(x) = x^2 + 1 / x^2 - 9 a)find y and x intercepts b) find the first derivative c) find any critical values d) find any local(relative) extrema e) find second derivative f) discuss the concavity g) find any

    asked by Gabby on April 28, 2013
  4. Calculus

    How many critical points does the function f(x) = [(x-2)^5][(x+3)^4] have? A. 1 B. 2 C. 3 D. 5 E. 9 --- Ok, these are my thoughts on this question: My impulse was to do derivative of the function. However, if I'm going to set the

    asked by Nikki on May 10, 2010
  5. Calculus c

    Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis

    asked by Madeline on December 19, 2012
  6. Calculus

    Let f be a twice-differentiable function defined on the interval -1.2 less than or equal to x less than or equal to 3.2 with f(1)=2. The graph of f', the derivative of f, is shown on the right. The graph of f' crosses the x-axis

    asked by Madeline on December 19, 2012

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