Grade 12 calculus help please?

Question

Determine an expression, in simplified form, for the slope of the secant PQ.

a) P(1,3), Q(1 + h, f(1 + h)), where f(x) = 3x^2

b) P(1,3), Q(1 + h, (1 + h)^3 + 2)

c) P(9, 3), Q(9 + h, √9 + h)
** For question c), both 9 + h are under the square root

Answer 1

(a)

Step 1:

The function is .

Two points on the function are and .

The slope of the secant  is .

Step 2:

The slope of the secant :

Substitute points and in .

Solution :

The slope of the secant is .

Answer 2

(b)

Step 1:

Two points on the function are and .

The slope of the secant  is .

Step 2:

The slope of the secant :

Substitute points and in .

Solution :

The slope of the secant is .

Answer 3

(c)

Step 1:

Two points on the function are and .

The slope of the secant  is .

Step 2:

The slope of the secant :

Substitute points and in .

Rationalize the numerator.

Solution :

The slope of the secant is .