Find an equation of the line that is tangent to the graph of f and parallel to the given line..

Question

thatonegirl_ · Answer

$$f(x)=3x^3$$
$$y=9x+9$$

campbell_st · Answer

ok... so I'd expect this is from a calculus course. 

you need to find the point of contact between the tangent and curve

you know the slope of the tangent is 9. 

so differentiate f(x) . This will give the equation for the slope of the tangent at any point on the curve. 

then let f'(x) = 9  and solve for x. 

substitute this value into the original function to find f(x)

then you will have a point (x, f(x)) and a slope m = 9

you will then be able to find the equation of the tangent. 

Hope it makes sense.

ajspeller · Answer

$$f'(x)=9x^2$$
Solve$$9=9x^2$$
use the point (x,f(x)) with slope, m=9 into the point slope formula
$$(y-f(x))=m(x-x) $$ where the second x is the x from (x,f(x))

thatonegirl_ · Answer

Thank you both!