Calculus

We are calculating the slope of the function f(x) = sqrt(x) at x = 4.

f(4) = 2
f(4+h) = sqrt(4 + h)

[f(4+h) - f(4)]/h =?


You have to pick a small h,and calculate it. Then pick an even smaller value and calculate it again. That's called taking the limit as h-> 0

If you pick h=0.1, you get a slope of
0.2484
If you pick h=0.01, you get a slope of 0.2498
Try an even lower value of h and you will see the trend to the limit.
The exact value of the slope, using the formula for the derivative at x=4, is (1/2)/(sqrt 4) = 1/4

  1. 👍
  2. 👎
  3. 👁

Respond to this Question

First Name

Your Response

Similar Questions

  1. algebra

    am I right? 1. Simplify radical expression sqrt 50 5 sqrt ^2*** 2 sqrt ^5 5 sqrt ^10 5 2. Simplify the radical expression sqrt 56x^2 28x 2x sqrt 14*** 2x sqrt 7 sqrt 14x2 3. Simplify the radical expression. sqrt 490y^5w^6 2 sqrt

  2. math;)

    Find the unit vector in the direction of u=(-3,2). Write your answer as a linear combination of the standard unit vectors i and j. a. u=-3[sqrt(13)/13]i+2[sqrt(13)/13]j b. u=-3[sqrt(5)/5]i+2[sqrt(5)/5]j c.

  3. algebra

    Simplify: 2 sqrt (3) + 6 sqrt(2) - 4 sqrt(3) + sqrt (2) a) 8 sqrt(2) - 3 sqrt(3) b) 6 sqrt(2) - 8 sqrt(3) c) 5 sqrt(6) d) 7 sqrt(2) - 2 sqrt(3) the answer i picked was d

  4. calc: avg value

    Find the average value of the function "f(x) = x^2 sqrt(1+x^3)" on the interval [0,2]. and this is what i did.. please check for mistakes. thanks :D f(x) = x^2 sqrt(1+x^3), [0,2] f ave = (1/(b-a))*inegral of a to b for: f(x) dx f

  1. Math

    The function f(x)=(x-5)^2+2 is not one-to-one. Identify a restricted domain that makes the function one-to-one, and find the inverse function. a. restricted domain: x>or=5; f^-1(x)=5-sqrt(x-2) b. restricted domain: x>or=5;

  2. algebra

    Simplify: sqrt (21) (sqrt(7) + sqrt(3)) a) 7 sqrt (3) + 3 sqrt(7) b) 7 sqrt(3) + sqrt (3) c) sqrt (210) d) sqrt (147) + sqrt (63)''. a

  3. Math:)

    A person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is centered at the origin. What is the exact value of the position of the rider after the carousel rotates

  4. ap calculus

    Which of the following definite integrals gives the length of y = e^(e^x) between x=0 and x=1? All the answers are preceded by the integral sign from 0 to 1. (a) sqrt[1 + e^(2*(x+e^x))] dx (b) sqrt[1 + e^(4x)] dx (c) sqrt[1 +

  1. math

    Find the slope m of the tangent to the curve y = 5/ sqrt (x) at the point where x = a > 0. what is the slope?

  2. calculus

    The point on the curve for y = sqrt(2x+1) at which tangent is perpendicular to the line y = -3x + 6 is.... a. (4, 3) b. (0,1) c. (1, sqrt3) d. (4, -3) e. (2, sqrt 5) I'm not sure, but do you find the perpendicular slope (1/3) set

  3. Algebra

    A square root function has a domain of x greater than or equal to -4 and range of y grreater than or equal to 2. Which of the equations below match this description? A. y= sqrt x-4 +2 B. y= sqrt x+4 +2 C. y= sqrt x-2 -4 D. y= sqrt

  4. CALCULUS. Check my answers, please! :)

    The domain of f(x)=(1)/(sqrt(x^2-6x-7)) is (1, 7) [-1, 7] x > -1 or x < 7 ***{x < -1}U{x > 7} (-∞, -1]U[7, ∞) 2. In which of the following is y a function of x? I. y^2=9-x^2 II. |y|=x III. y=(sqrt(x^2))^3 I only II only III

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