## Precalculus Textbook 8th Edition Section 2.1 Exercise 78 Solution

**Question**:

Let f(x) = x^{2}, g(x) = 3x + 2, h(x) = 7x – 3, k(x) = mx + b and l(x) = x^{3}.

(a) Compute the average rate of change of f from x = 1 to x = 3.

(b) Compute the average rate of change of f from x = 2 to x = 5.

(c) Compute the average rate of change of f from x = a to x = c.

(d) Compute the average rate of change of g from x = 1 to x = 3.

(e) Compute the average rate of change of g from x = 1 to x = 4.

(f) Compute the average rate of change of g from x = a to x = c.

(g) Compute the average rate of change of h from x = a to x = c.

(h) Compute the average rate of change of k from x = a to x = c.

(i) Compute the average rate of change of l from x = a to x = c.

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**Solution**:

(a) The given function is f(x) = x^{2}.

Average Rate of Change from x = 1 to x = 3 is

(b) The given function is f(x) = x^{2}.

Average Rate of Change from x = 2 to x = 5 is

(c) The given function is f(x) = x^{2}.

Average Rate of Change from x = a to x = c is

(d) The given function is g(x) = 3x + 2.

Average Rate of Change from x = 1 to x = 3 is

(e) The given function is g(x) = 3x + 2.

Average Rate of Change from x = 1 to x = 4 is

(f) The given function is g(x) = 3x + 2.

Average Rate of Change from x = a to x = c is

(g) The given function is h(x) = 7x – 3.

Average Rate of Change from x = a to x = c is

(h) The given function is k(x) = mx + b.

Average Rate of Change from x = a to x = c is

(i) The given function is l(x) = x^{3}.

Average Rate of Change from x = a to x = c is

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