Let , where is a real constant. The tangent to the curve at the point with abscissa…

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

Let

h(x)=k x^{3}+2x^{2}-3x+1

, where

k

is a real constant. The tangent to the curve

y=h(x)

at the point with abscissa

x=1

passes through the fixed external point

P(2,0)

. (i) Find the value of

k

. (ii) For this value of

k

, write the equation of the tangent at

x=1

. (iii) Using the same value of

k

, obtain the equation of the normal to the curve at

x=1

and determine the point where this normal meets the

y

-axis.