Calculus
posted by Preston .
Find the slope of the tangent line to the curve y = (x^2 8)^6 at x = 3, and
write the equation of the tangent line.

Take the derivative.
y'=6(x^28)^5 * 2x
at x=3, put that in, and compute y'
equation: y=y' x + b
you have y'. you know x, and can compute y (original equation), so can compute b from that equation.
Respond to this Question
Similar Questions

Help Calc.!
original curve: 2y^3+6(x^2)y12x^2+6y=1 dy/dx=(4x2xy)/(x^2+y^2+1) a) write an equation of each horizontal tangent line to the curve b) the line through the origin with the slope .1 is tangent to the curve at P. Find x and y of point … 
please help; calc
original curve: 2y^3+6(x^2)y12x^2+6y=1 dy/dx=(4x2xy)/(x^2+y^2+1) a) write an equation of each horizontal tangent line to the curve b) the line through the origin with the slope .1 is tangent to the curve at P. Find x and y of point … 
Need help fast on calc
original curve: 2y^3+6(x^2)y12x^2+6y=1 dy/dx=(4x2xy)/(x^2+y^2+1) a) write an equation of each horizontal tangent line to the curve b) the line through the origin with the slope .1 is tangent to the curve at P. Find x and y of point … 
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 … 
calculus
Consider the curve defined by 2y^3+6X^2(y) 12x^2 +6y=1 . a. Show that dy/dx= (4x2xy)/(x^2+y^2+1) b. Write an equation of each horizontal tangent line to the curve. c. The line through the origin with slope 1 is tangent to the curve … 
Calculus
Please help this is due tomorrow and I don't know how to Ive missed a lot of school sick Consider the curve given by the equation x^3+3xy^2+y^3=1 a.Find dy/dx b. Write an equation for the tangent line to the curve when x = 0. c. Write … 
Calculus
1) An equation of the line contains points (7/9, 7) and (7/9) is 2) Find the slope of the line tangent to the curve y=x^2 at the point (0.6, 0.36) and find the corresponding equation of the tangent line 
Math
Suppose f(x)=5/(x2). f'(5)=5/9. Use this to find the equation of the tangent line to the curve y=5/x2 at the point (5,(5/3)). write your answer in the form y=mx+b where m is the slope and b is the yintercept. The equation of the … 
Calculus AB
Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x1)e^x. For which value of x is the slope of the tangent line to f positive? 
Calculus AB
Could someone please help me with these tangent line problems?