find the gradient of the tangent to the curve y=3x^2+2x-1 p(1,4)

Answer 1

Slope = gradient if tangent line = dy/dx = m

In this case:

dy / dx = m = 3 • 2 x + 2 = 6 x + 2

In point where x = 1

m = 6 x + 2 = 6 • 1 + 2 = 6 + 2 = 8

Point slope equation of straight line is:

y − y1 = m ( x − x1 )

In this case:

x1 = 1 , y1 = 4 , m = 8

so

y − y1 = m ( x − x1 )

y − 4 = 8 ( x − 1 )

y − 4 = 8 x − 8

Add 4 to both sides.

y = 8 x - 4

Answer 2

My typo.

Slope = gradient of tangent line = dy/dx = m