Post a New Question

calculus anti-derivation

posted by .

Given that the graph of f(x) passes through the point (2,5) and that the slope of its tangent line at (x, f(x))is 3x+5, what is f(3) ?

  • calculus anti-derivation -

    if dy/dx = 3x+5 , then
    y = (3/2)x^2 + 5x + c

    when x=2, y = 5
    5 = (3/2)(4) + 10 + c
    5 = 6 + 10 + c
    c = -11

    f(x) = (3/2)x^2 + 5x - 11
    f(3) = (3/2)(9) +15 - 11 = 35/2

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. cal

    Equations of the tangent lines to hyperbola xy=1 that pass through point (-1,1) I know the graph of y=1/x but not sure about the tangent lines at given point. Are the lines tangent to (1,1) and (-1,-1)?
  2. Math- calculus

    Given f(x) = x ^ 3 - x ^ 2 -4x +4 Find the zeros of f. Write an equation of the line tangent to the graph of f at x = -1 The point (a,b) is on the graph of f and the line tangent to the graph at (a,b) passes through the point (0,-8) …
  3. calculus

    If the graph of f passes through the point (1, 0) and the slope of the tangent line at(x, f(x)) is 4x − 3, find the value of f(2).
  4. math

    i have more than one question so if u no any of the answers please tell me 1.) write the point-slope form of the equation of the line with slope -2 passing through the point ( -5, -9). 2.) write the point-slope form of an equation …
  5. College Calculus

    Let f(x) = 3x^2 - 2x + 1 a) write an equation of the line going through the points (1, f(1)), and (2, f(2)). b) Find a point on the graph of f where the tangent line to the graph has the same slope as the line in part (a). Write the …
  6. Calculus

    1. Given the function f defined by f(x) = x^3-x^2-4X+4 a. Find the zeros of f b. Write an equation of the line tangent to the graph of f at x = -1 c. The point (a, b) is on the graph of f and the line tangent to the graph at (a, b) …
  7. calculus

    find a function f given that (1) the slope of the tangent line to graph of f at any point P(x,y) is given by dy/dx=3xy and (2) the graph of f passes through the point (0,2)
  8. Calculus

    Sketch a graph of the parabola y=x^2+3. On the same graph, plot the point (0,−6). Note there are two tangent lines of y=x2+3 that pass through the point (0,−6). The tangent line of the parabola y=x^2+3 at the point (a,a^2+3) …
  9. Math

    Find the function f, given that the slope of the tangent line at any point (x,f(x)) is f '(x) and that the graph of f passes through the given point. f '(x)=6(2x-7)^5 at (4, 3/2)
  10. Math - calc

    Given that the graph of f(x) passes through the point (6,3) and that the slope of its tangent line at (x,f(x)) is 2x+6, what is f(5)?

More Similar Questions

Post a New Question