Calculus please help??
Find the equation of the line tangent to
f(x) = 3x^2 + 2x + 7 at the point (1, 12).

Question

Calculus please help??
Find the equation of the line tangent to
 f(x) = 3x^2 + 2x + 7 at the point (1, 12).

mertsj · Answer

@VIbarguen1 Can you find the first derivative?

anonymous · Answer

f'(x)= 6x+2

mertsj · Answer

That is the slope function.  To find the slope of the tangent at (1,12) replace x with 1.  That will be the slope.  Then find the equation of the line with that slope which contains the point (1,12).  That will be the equation of the tangent at the given point.

anonymous · Answer

so the slope is 8

anonymous · Answer

is there a formula I can use to find the equation or is it just guessing?

mertsj · Answer

Do you remember in algebra 1 when you learned that the equation of a line, in point slope form is:
$$y-y _{1}=m(x-x _{1})$$

anonymous · Answer

yes

mertsj · Answer

Replace m with 8, replace x_1 with 1, replace y_1 with 12

anonymous · Answer

y-12=8(x-1)
y-12=8x-8
y=8x-8+12
y=8x+4

is that the answer?

mertsj · Answer

yep

anonymous · Answer

thnx soo much