Question

What is the y-intercept of the line that is tangent to f(x)=(3x^2-1)(x^2+2) when x=1? The answer is -16 but how?

Answer 1

Are you in calc?

Answer 2

what did you get as the derivative..?

Answer 3

I'm taking calculus and vectors.
So do I expand and simplify then find the derivative?

Answer 4

I did that and got f'(x)=12x^3+10x

Answer 5

that works.... the 1st derivative is essential...

you also need a point... you know x = 1 so substitute that value
into the original equation to get a y value for the point

(1, y)

when you get the derivative.... this is actually the equation of the slope
at any point on the curve...

so subsitute x = 1 into the derivative... and you have a slope

so now after the work you have a point and slope...which you need to find the
equation of the tangent.

Hope it makes sense

Answer 6

ok the derivative is correct.. so find

f'(1) =

Answer 7

f'(1)=22

Answer 8

great so m = 22

what is the point on the curve (1, ?)

Answer 9

so the point is (1,6)

Answer 10

great so the slope intercept form is

y = 22x + b

to find b, the y-intercept, subsitute the point and solve for b

6 = 22(1) + b

Answer 11

ok i understand it now! thanks a lot!