y= 2x^2 + 3x
a) i need to find the slope at x= -2
b) then i need to find the equation of the tangent line at x= -2
Differentiate the equation and get the value of y' in terms of "x"
1)Find value of y'(-2) by putting x = -2
at x = -2 , y=?
the equation of tangent can be given by
this euation should satisfy the for the point (-2,?)
, you know the value of m [it is, y'(-2) ]
use this two facts to find "c"
Hence equation is with you
y = -5x +c
At x =-2
y = 2(-2)^2 + 3(-2)
=8-6 = 2
this gives a point (-2,2) on the curve
So the tangent will pass through this point and hence this point satisfies its equation
y = -5x+c will pass through (-2,2)
Hence thew complete equation is