Posted by **Ronnie** on Saturday, June 19, 2010 at 1:06pm.

I have been struggling with this problem I cannot get the right answer. Please give me the steps to solve this problem.

Let f(x)= (2x-9)(x^2 + 6)

(A) Find the equation of the line tangent to the graph of f(x) at x=3

(B) Find the values(s) of x where the tangent line is horizontal.

- College Math -
**Reiny**, Saturday, June 19, 2010 at 5:11pm
I would expand the function first, then find the derivative.

f(x) = 2x^3 + 12x - 9x^2 - 54

f '(x) = 6x^2 + 12 - 18x

when x = 3

f(3) = -3(15) = -45

f '(3) = 6(9) + 12 - 18(3) = 12

A) so you have a slope of 12 and a point (3,-45)

Use y = mx + b to find the tangent equation

B) set 6x^2 - 18x + 12 = 0

and solve

Hint: divide both sides by 6, then it factors

- College Math -
**Anonymous**, Friday, June 25, 2010 at 4:58pm
Identify the variable, constant, and coefficient of the expression: –10k + 15

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