The sketch graph shows the curve of y = 3x² − x³. The marked point, P, has coordinates (2, 4).

a. Find:

i. The gradient function dy/dx

ii. The gradient of the curve at P

iii. The equation of the tangent at P

iv. The equation of the normal at P.

b. The graph touches the x-axis at the origin O and crosses it at the point Q.

Find:

i. The coordinates of Q

ii. The gradient of the curve at Q

iii. The equation of the tangent at Q.

c. Without further calculation, state the equation of the tangent to the curve at O.

Transcribed Image Text:

YA y = 3x -x Р 2, 4)