# Integration Long Questions (Question 1 & 2)

Question 1:
A curve with gradient function $5x-\frac{5}{{x}^{2}}$  has a turning point at (m, 9).
(a) Find the value of m.
(b) Determine whether the turning point is a maximum or a minimum point.
(c) Find the equation of the curve.

Solution:
(a)

(b)

(c)

Question 2:
A curve has a gradient function kx2 – 7x, where k is a constant. The tangent to the curve at the point (1, 3 ) is parallel to the straight line  y + x – 4 = 0.
Find
(a) the value of k,
(b) the equation of the curve.

Solution:
(a)
y + x – 4 = 0
y = – x + 4
m = –1

f ’(x) = kx² – 7x
Given tangent to the curve at the point (1, 3) parallel to the straight line
k (1)² – 7 (1) = –1
k – 7 = –1
k = 6

(b)