calculus

posted by .

Let f(x)=e^(x2). By the Mean Value Theorem, there exists a point c such that

f′(c)=f(6)−f(4)6−4

with c between 4 and 6. Approximate c to within two decimal places; we're asking you to approximate c, because you can't "solve" for c.

  • calculus -

    Your statement of
    f′(c)=f(6)−f(4)6−4
    desperately needs brackets to say
    f′(c)= ( f(6)−f(4) )/(6−4)

    f(6) = e^36 = 4.31123x10^15 , rather large
    f(4) = e^16 = only 8886110.52

    ( f(6) - f(4) )/2 = 2.1556x10^15

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    Estimate f′(−3) where f(x) = x^3 + 8x^2 − 10x − 1 to within one decimal place by using a small enough interval. f′(−3) ≈
  2. calculus

    Consider the interval I=[6,7.6]. Break I into four subintervals of length 0.4, namely the four subintervals [6,6.4],[6.4,6.8],[6.8,7.2],[7.2,7.6]. Suppose that f(6)=19, f′(6)=0, f′(6.4)=−0.5, f′(6.8)=−0.1, …
  3. Grade 12 Calculus

    Evaluate each of the following. Show all your calculations. a) f'(3) if f(x)  = x^4 − 3x b) f' (−2) if f(x) = 2x^3 + 4x^2 − 5x + 8 c) f" (1) if f(X)  = −3x^2 − 5x + 7 …
  4. calculus (gr 12)

    Evaluate each of the following. Show all your calculations. a) f'(3) if f(x)  = x^4 − 3x b) f' (−2) if f(x) = 2x^3 + 4x^2 − 5x + 8 c) f" (1) if f(X)  = −3x^2 − 5x + 7 …
  5. calculus (gr 12)

    Evaluate each of the following. Show all your calculations. a) f'(3) if f(x)  = x^4 − 3x b) f' (−2) if f(x) = 2x^3 + 4x^2 − 5x + 8 c) f" (1) if f(X)  = −3x^2 − 5x + 7 …
  6. Math

    16) Consider the function f(x)=2x3−6x2−90x+5 on the interval [−6,7]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists at least one c in the open interval …
  7. Math

    17) Consider the function f(x)=3x3−3x2+4x+2 Find the average slope of this function on the interval (−3,5). By the Mean Value Theorem, we know there exists a c in the open interval (−3,5) such that f′(c) is …
  8. Calculus

    Let f(x)=5x2+5x−12. Answer the following questions.Find the average slope of the function f on the interval [−1,1].Verify the Mean Value Theorem by finding a number c in (−1,1) such that f′(c)=m¯¯¯.
  9. calculus

    F.(0) (10 puntos posibles) C1   What is limh→0cos(π6+h)−cos(π6)h?
  10. Calculus 1

    Use Newton's method to approximate the indicated root of the equation correct to six decimal places. The root of x^4 − 2x^3 + 5x^2 − 5 = 0 in the interval [1, 2]

More Similar Questions