Math
posted by Vanessa .
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(2x7)^5 at (4, 3/2)

f=INT f= (2x7)^6 + C
now find C
3/2 = (2*47)^6 + C
C=1/2 
if dy/dx = 6(2x7)^5
y = (6/6) (2x7)^6 (1/2) + c
y = (1/2)(2x7)^6 + c
but (4 , 3/2) lies on it, so
3/2 = (1/2)(1)^6 + c
3/2 = 1/2 + c
c = 1
f(x) = (1/2)(2x7)^6 + 1
Respond to this Question
Similar Questions

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)? 
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) … 
math
i have more than one question so if u no any of the answers please tell me 1.) write the pointslope form of the equation of the line with slope 2 passing through the point ( 5, 9). 2.) write the pointslope form of an equation … 
Calculus
1. Given the function f defined by f(x) = x^3x^24X+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) … 
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) 
calculus antiderivation
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
1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))? 
Algebra
1.Write an equation in slope intercept form of the line that passes through the given point and is parallel to the graph of the given equation. (2,2);y=x2 A.y=2x*** B.y=2x C.y=1/2x D.y=x 2.Write an equation in slope intercept … 
Algebra
1.Tell whether the sequence is arithmetic. If it is, what is the common difference? 
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)?