Find the equation of the tangent line at x = 2 for f(x) = 4 + x - 2x^2 - 3x^3. Write the answer in the form of y=mx+b.

Question

Find the equation of the tangent line at x = 2 for f(x) = 4 + x - 2x^2 - 3x^3. Write the answer in the form of  y=mx+b.

campbell_st · Answer

do you know the 1st derivative.... f'(x)...?

anonymous · Answer

is it 2*2x^2-1= 4x

campbell_st · Answer

not the derivative f'(x) = 1 -4x - 9x^2

this is the equation of the slope of the tangent at any point on the curve

you have the specific case of x = 2

so evaluate 

f'(2)  which means substitute x = 2 into the derivative and get a number answer. 

you will also need to point on the curve... so  substitute x =2 into the original equation to find y. 

then you will have, m x and y

substitute into 

y = mx + b

and solve for b... this will be the equation of the tangent. 

hope this helps

anonymous · Answer

im getting the mx but when I solve for b, it is not coming out right. im getting 17

campbell_st · Answer

ok, what did you get for f'(2) ...?