From first principles (ie using the tangent slope method), find the slope of the following curves at the given value of x.

Question

f(x)=2x^2−6x at x = 3

f(x)=2x^2-6x

f(x+h)= 2(x+h)^2-6(x+h)

=2x^2+4xh+2h^2-6x-6h

lim h-->0 f(x+h)-f(x)/h

=2x^2+4xh+2h^2-6x-6h - (2x^2-6x)

=4xh+2h^2-6h/h

=h(4x+2h-6)/h

=lim h -->0 = 4x+2h-6

4x+2(0)-6
=4x-6

at x=3

f(3)=4x-6
=4(3)-6
=6

Im I doing this correct?

Answer 1

you are right on.

Answer 2

Are you sure? Someone told me I'm doing this wrong