# Urgent Calculus Help 2

posted by .

Find the equation of the tangent line to the graph of f(x) = 6x ln(x + 4) at x = 2.

• Urgent Calculus Help 2 -

dy/dx = 6x d/dx [ln(x+4)]+ 6 ln(x+4)

= 6 x /(x+4) + 6 ln(x+4)
so at x = 2
dy/dx = slope = m = 12/ln(6) + 6 ln (6)

but ln (6) = 1.79
so use that to find the slope m

then we have
y = m x + b and we know m

find y at x = 2
y= 12 (1.79) = 21.5
so use that
21.5 = 2 m + b
we know m, solve for b
the end

• Urgent Calculus Help 2 -

Thank you!

• Urgent Calculus Help 2 -

You are welcome.

## Similar Questions

1. ### Calculus

55. Find an equation of the tangent line to the graph of f(x) =x^3 - 2x + 1 a) at (2,5); b) at (-1,2); c) at (0,1). I believe the answers are: a) y= (3/2 x) - (3/2) b) No solution c) No solution For each function, find the points on …
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

find the equation of a quadratic function whose graph is tangent at x=1 to the line whose slope8, tangent at x=-2 to solve the line with slope-4 and tangent to the line y=-8
4. ### cal

find the equation of a quadratic function whose graph is tangent at x=1 to the line whose slope8, tangent at x=-2 to solve the line with slope-4 and tangent to the line y=-8 find the equation of the tangent lines at x=1 and x=-2 graph …
5. ### calculus

5. Let f be the function given by f(x) = x3- 7x + 6. a. Find the zeros of f b. Write an equation of the line tangent to the graph of f at x = -1 c. Find the x coordinate of the point where the tangent line is parallel to the secant …
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

Let f(x)=3x^4-2x^2+3 a) find f'(x) Answer: f'(x)=12x^3-4x b) find the slope of the line tangent to the graph of f at x=3. Answer:312 So I got those firs two right but what I need help with is part C which is c) find an equation of …
8. ### Calculus

The function g is defined for x>0 with g(1)=2, g'(x)=sin(x+1/x), and g"(x)=(1-1/x^2)cos(x+1/x). A. Find all values of x in the interval 0.12<=x<=1 at which the graph of g has a horizontal tangent line. B. On what subintervals …
9. ### Calculus AB

Sorry but I've got a lot of problems that I don't understand. 1) Let f(x)= (3x-1)e^x. For which value of x is the slope of the tangent line to f positive?