Question

For `f(x) =4x^3+12x^2+9x+7`, what is the equation of the line tangent to `x =-3/2`?

Answer 1

`y=7`

Explanation:

`•color(white)(x)m_(color(red)"tangent")=f'(x)" at "x=-3/2`

`f'(x)=12x^2+24x+9`

`rArrf'(-3/2)=12(-3/2)^2+24(-3/2)+9=0`

`rArr"tangent is parallel to the x-axis"`

`f(-3/2)=4(-3/2)^3+12(-3/2)^2+9(-3/2)+7`

`color(white)(f(-3/2))=7`

`rArr"equation of tangent is "y=7`
graph{(y-4x^3-12x^2-9x-7)(y-0.001x-7)=0 [-20, 20, -10, 10]}